Well, funnily enough when James VI and I became the first Stuart king in England, he was perceived as *beneficial* to the Howards. This all comes down to what happened after that battle. The House of Howard has a rollercoaster history.

John Howard 1st Duke of Norfolk was ennobled from gentry to duke as a supporter of Richard III. The patent for the title cited his direct descent from Thomas de Mowbray 1st Duke of Norfolk through his mother, thereby making him one of the few remaining heirs to the de Mowbray family that previous held the title. Obviously that didn't play out. John Howard died at the Battle of Bosworth with his patron. He left behind his son, Thomas Howard, who had fought in the battle. Henry VII could have easily had Thomas Howard killed as well. However, it's worth understanding the character of Henry VII. Unlike his son, who always saw himself more as a knight, Henry VII was less war-hungry and had a notable interest in financial policy. He was also quite strategic. As part of his strategy to end the Wars of the Roses, classically symbolised by his marrying Elizabeth of York and the Tudor rose, he wanted to make use of the people left behind. However, Thomas Howard was not allowed to be 2nd Duke of Norfolk until later, he had to prove his capacity to get on side.

This history was clearly in mind for Thomas, and his son the future 3rd Duke. They got the recognition for the de Mowbray hereditary claim to the Earl Marshalship, which both of them held in turn as they did the office of Lord High Admiral. Flodden was a great example of this. Conformity paid off. However, this is where Henry VIII decided to become involved in the Reformations of Religion.

The Howards were known to be somewhat conservative, that is Catholic sympathising. But the 3rd was a pragmatist, and he had a familial alliance with Anne Boleyn. Even when his niece was tossed, he saw which way the wind was blowing and avoided that fate too, not his most honourable moment but it worked. He even crushed the Pilgrimage of Grace, a Catholic protest against Henry. When his other niece Katherine Howard went down too however, things weren't looking good His stepmother had also been implicated, or at least accused, in facilitating the accused adultery. The family reputation was in danger. Unfortunately for him, the 3rd Duke's son the Earl of Surrey (courtesy title from the 2nd Duke), made the mistake of quartering his arms with those of Edward the Confessor. It was harmless arrogance, and there was a scholarly heraldic argument for it, but Henry VIII was by this time a paranoid man who had no issues executing his friends and advisors. That conservative inclination also meant there was a more protestant faction that was glad to see him go. The Earl of Surrey was tried for the arms, because Henry had suspicions of a usurping plot, and executed. The 2nd Duke was imprisoned and was due to be executed except for Henry's death. It was consider a kind of courtesy not to execute prisoners at the start of a new reign. Then when Mary became queen after Edward's untimely death, Thomas Howard 3rd Duke of Norfolk became a free man.

Of course, Mary also did not last long. But Elizabeth I, like Henry VII, tried to make a more unifying start. She accepted Surrey's sons Thomas and Henry. Thomas Howard was now 4th Duke of Norfolk at this time, which gave him a certain protective status. Thomas Howard was an interesting person really. It's not clear if he actually was Catholic in any real sense, although he was certainly not an enthusiastic Protestant reformer. His brother Henry, who was probably an actual Catholic, was suspected of having led him along the path he would take. The 4th Duke, frustrated by his limited power at court, agreed to a plan where he would marry Mary Queen of Scots and become king. The associated plot was foiled and the 4th Duke was executed. Henry Howard, although some thought him worse than his brother, remained alive. During the rest of Elizabeth's reign he relied on a combination of a pension from the Queen and income from lectures he gave. He devoted himself to scholarship, partly as a pass time and partly it seems on the hope of rebranding himself as a trustworthy and wise figure. He was later under-threat over more involvement with Mary, but nothing about his interactions could be proven treasonous. Later, his associations with Edward de Vere 17th Earl of Oxford and Charles Arundell on mutual interest in Catholicism were discovered when Oxford betrayed the others to save his own skin. Henry Howard was arrested but escaped execution again. He was smart enough to avoid anything particularly illegal. Meanwhile, his nephew Phillip Howard, 13th Earl of Arundel was also arrested on Catholicism-related treason to do with Mary Queen of Scots; he was accused of being part to the Throckmorton Plot. Henry Howard busied himself with flattery, not only of Elizabeth but also petitioning both William Cecil Lord Burghley and Robert Devereux 2nd Earl of Essex, looking for patrons. When Burghley's son Robert and Essex came into conflict, he initially sided with Essex and made himself a key advisor. But slippery as he was, and much in the spirit of the 3rd Duke's evasions, when it became clear Essex was on a self-destructive path, he presented himself to Robert Cecil.

By this time, Henry Howard was already managing part of Essex's secret correspondence with James VI of Scotland, Elizabeth's most likely heir. He offered to help Robert Cecil with the same project, and James endorsed him as an intermediary. So when James did arrive in England, Henry Howard was one of the people involved in making sure it happened. He and Robert Cecil were summoned early on to meet with James in the north. For a brief period, Northampton acted as James' secretary while he was still travelling south. He became a Privy Councillor, he was involved in the trials of the Main and Bye plots where he helped to disgrace and imprison his former rivals Walter Raleigh and George Brooke, in 1604 he was given a proper title as Earl of Northampton and Baron Marnhull, and he took the office of Lord Warden of the Cinque Ports. Despite his likely Catholicism, perhaps almost because of it, he was entrusted with being one of the negotiators for what is now known as the Somerset House Conference, where England and Spain ended the war that had begun with Mary Queen of Scots and the Armada.

And it wasn't just him. There were his relatives Charles Howard Earl of Nottingham and Thomas Howard, the 4th Duke's son who became Earl of Suffolk, they had both already made success under Elizabeth but for Suffolk certainly James accession marked a new high point. And Northampton made sure to introduce James to all his Howard relatives including his great nephew, Phillip's son the new 14th Earl of Arudnel. The Venetian ambassador said "The King continues to support those houses and persons who were oppressed by the late Queen" (Calendar of State Papers Relating to English Affairs in Venice, May 1603). It was helpful that James VI and I was relatively tolerant and curious about Catholicism, so he wasn't as fussy about the family history as long as they behaved themselves with him. And Northampton's brother and nephew had died partially due to James' mother, it would be a bad look to not have any sense of sympathy to them.

So, in conclusion, by the time it came round to it, people were talking more about Catholicism and Mary Queen of Scots than the Battle of Flodden. In that vein, there was more concern about the Howard not being loyal enough to England than concern about them being any kind of anti-Scots warmongers. James accession automatically ruled out war between the kingdoms, and he was strictly against the border skirmishes in the north. The foreign policy debate of the time was much more with Spanish and secondarily the Austrian Hapsburgs, and all of the Howards at that time appear to have been more or less supportive of that peace. But of course, as before things could always change later on...