While reading the (French) wikipedia page about the Burgundian Wars in the 1470's, it is said that Duke Charles of Burgundy declared himself freed from the authority of the King of France. In 1473, Duke Charles and Emperor Frederic III of the HRE met at Trèves, and the latter accepted to let Charles use his possessions within the Empire to create his own kingdom (if I understood correctly).
Finally, it says that Frederic III broke the negotiations and fled the night before the coronation, along with his son Maximilian who was supposed to marry Mary of Burgundy to seal the deal. This event cancelled the coronation and crushed Charles dreams of a united Burgundian Kingdom
Unfortunately, the article does not explain the reasons that lead Frederic III to break the negotiations and flee. What happened between the two men? What events led to the Emperor doing such a dick move and run away as Charles was about to be crowned?
For the most part, the emperor's flight remains a mystery. We can only make assumptions. I am mostly going to use R. Vaughan's biography of Charles the Bold (1973).
First of all, it must be specified why the two men encountered: Charles the Bold's main objective was not to have a kingdom of his own but to be crowned King of the Romans. Indeed, his wish was that Maximilian, Frederick's only son and heir, married Mary, his only daughter and heiress, so that Maximilian would become his heir. On the death of Frederick, the Empire would pass to Charles, who would crown Maximilian King of the Romans, making him in turn the heir to the Empire.
Why would the emperor accept such a proposal? Actually, it was a pretty good offer for him. The duke of Burgundy was perhaps the most powerful prince in Europe, second in wealth (behind the king of France), and the most feared, above all within the Empire itself (for instance, in 1468, when he sacked and burned the rebellious town of Liège, Aachen offered him its keys). Such an alliance with the powerful House of Burgundy would have secured the Habsburg claims to the imperial throne. Futhermore, the future Habsburg-Burgundian monarchs would have been rulers of both Austria in the East and the Burgundian lands in the West, making them the most powerful territorial rulers within the Empire, surrounding it. They would have gained a great political power and undermined the power of the Electors. Frederick III has often be described as a weak ruler, but a great dynast: the interests of the Habsburg dynasty inevitably sparked his interest in this offer.
Duke Charles of Burgundy, for his part, was obsessed with his personal glory and what would be left of him in history, and he was passionate about Roman history (and Alexander the Great). Surely he wanted to restore the imperial title to its former glory.
But when they finally meet in October 1473 at Trier (Trèves), Frederick was no longer interested in this project, at least for now. The first days of their encounter were seen as a humiliation by several members of the imperial court. Charles was richly dressed, he organized an incredible feast, and rejected every ceremonial aspect that would have made him inferior to the emperor. We can suppose this wasn't well received. Furthermore, even if the duke of Burgundy bought some of them, the prince-electors were not very enthusiastic about this prospect. Charles didn't understand the German customs, and the electors were relegated to the background during these talks.
It quickly became clear that the Emperor wouldn't crown Charles king of the Romans. Charles himself was about to leave Trier, until the emperor's men asked him to stay.
Indeed, in the meantime, during talks with the chancellor of Burgundy, Frederick agreed to crown Charles, not as king of the Romans, but of a new kingdom, which would include all the lands that Charles possessed within the Empire, plus the duchies of Lorraine (between his northern and southern possessions) and Savoy (south to his possessions, already an ally) and some bishoprics. Charles would take the title of "King of Burgundy". His French lands, however, would remain separate.
This idea of a new Burgundian kingdom wasn't new. Frederick III had already suggested to duke Philip the Good, Charles's father, that he wanted to make him king (of Brabant or Friesland), in order to follow the prestige the duke of Burgundy had gained within the Empire, now that he ruled over the entire Low Countries. But Philip refused, arguing that if he had to be king, it would be over a larger kingdom uniting all his possessions. Furthermore, unlike his son, Philip remained a French prince who never paid hommage to the Emperor, even if later, faced to French envoys, he would declare that, if he had wanted, he would have been king.
This time, the prospect of a new kingdom was much more appealing for Charles, even if he had asked his chancellor and his other negociators not to speak of it until it was certain that he would not receive the Roman title. Very interested in the administration of his territories, the creation of a "Kingdom of Burgundy" would allow him to carry on the centralization of power in his Burgundian state. Above all, he would gain in prestige, even if he was already perhaps the most powerful prince in the Christendom, becoming a king at last, and becoming suzerain to the dukes of Lorraine and Savoy, which would perhaps allow him to later march south in order to conquer Provence and then nothern Italy (according to Vaughan, he was very interested in the conquest of Milan), recreating something close to the ancient kingdom of Lothair.
As you can imagine, the prospect of Charles the Bold being a new king of Burgundy was annoying to a vast bunch of people, perhaps as much as the idea of him as Holy Roman Emperor:
In fact, Frederick III was surrounded by people who disapproved his plans. The most incredible thing is not his flight, it is that he agreed to the coronation in the first place (says the Belgian historian J.-M. Cauchies, 1996).
Moreover, Charles and Frederick remained opposed on many subjects: Charles the Bold was still friend with Frederick I, Elector Palatine and with Venice, both enemies of the emperor. By the way, Charles had bought lands (Upper Alsace, Brisgau and Sundgau) in 1469 from Sigismund, duke of Austria, the emperor's cousin. But Sigismund now wanted these lands back, which Charles refused, to the displeasure of Frederick III.
Nevertheless, all was already prepared for the coronation who should have taken place in the cathedral of Trier on 18 November 1473, then delayed until Frederick III and his son Maximilian left Trier on the morning of 25 November, as you pointed out. The banners were made; the crown and the sceptre of the new king were forged. But they weren't used, even if the coronation appeared imminent, so much that on 13 November, Margrave Albert of Brandenburg wrote Duke William of Saxony that Charles was already crowned.
Eventually, for the reasons mentioned above, this coronation did not take place. If it was truly a surprise, the negociations were not abruptly ended as Wikipedia seems to put it. Frederick announced his intended departure the day before. The morning he left, according to the councillors of the margrave of Brandenburg, the Burgundian Peter von Hagenbach followed him, asking him to stay a little longer. The emperor and his son waited for the duke but Charles didn't come quickly enough.
This is a failure for Duke Charles, but not irreparable. From now on, he would form a kingdom of his own. A month later, at Thionville, he created the Parlement of Mechelen, a court of appeal for all the Burgundian Low Countries. In January 1474, in a speech to the Estates of Burgundy, the duke mentioned the old kingdom of Burgundy, "usurped by the French". From 1475, he would be refered to as "my most dreaded and sovereign lord the duke of Burgundy", implying he should now be considered as a true sovereign by divine grace. Later this year, he would conquer the duchy of Lorraine, finally ruling over a continuous territory. Rumour had it that he proclamed the Lorrainer town of Nancy would become the capital of his new kingdom. It is before the towns of this town that he would met his death a year later, defeated by the armies led by the duke of Lorraine René II.
Until the end, the duke kept in touch with the emperor. Even during the siege of Neuss (1474-1475), where he helped Frederick of the Palatinate, against the Holy Roman Emperor who eventually joined the City of Cologne to defend Neuss. Both men still hoped an alliance could be made.
In the end, the marriage of Mary and Maximilian took place as intended, after Charles the Bold's death. The projects of both Charles and Frederick would be fulfilled by their common great-grandson, Charles V. Ruler of both the Burgundian and Austrian lands (and Spain), he would become the most powerful emperor the HRE had known for centuries. Born in Ghent, duke of Burgundy at age 6, feeling more Burgundian than Austrian or Spanish (he would always ask to be burried in Dijon, with the other dukes of Burgundy, if the duchy of Burgundy itself was to be recovered - it would never be), Charles V (who took his great-grandfather's name) would be presented by Burgundian propaganda as Charles the Bold reborn.
Speaking of the coronations as kings of Spain of both Philip the Handsome and his son Charles V, J. Dumont writes: "the lion (is) finally crowned" (the lion being the heraldic figure of the house of Burgundy).