In other words, if there were Latinos (Mexicans, Central or South Americans, Spanish Caribbean) or Filipinos living in Spain anytime during the Franco regime (1936-75), would they have been especially oppressed (more so than the average Spaniard) under the Franco dictatorship, possibly out of a perceived "revenge" for their home countries having broken away from the old Spanish Empire?
By the same token, did Franco ever attempt to, well, retake any of the Spanish Empire's former colonies, or would factors at the time (not least US predominance—it's the same power that defeated them in 1898 after all) have prevented Franco from even attempting this?
So, the first part of your question is really interesting, but I don't have a good answer. I've never come across primary or secondary accounts of the experiences of Latin Americans or other former colonial subjects in Francoist Spain. Speculatively, I don't think revenge for independence would be a motive for especial repression, but there certainly is potential for both racial and political causes, depending on the individuals in question. Would an anti-communist, European-appearing Latin American elite be discriminated against? I suspect not. Would a mixed-race or native individual with left-wing politics be? Certainly, although I'd wonder how many there would actually be in Francoist Spain. One potential avenue for exploring this question would be the fates of the Latin Americans who volunteered to fight for the Republic, of which there were several thousand, some of whom were captured and may have received different treatment. Sadly, while I know some good resources on these individuals, I don't have access to them at the moment.
I can be a bit more concrete regarding Francoist imperial ambitions. Restoring Spanish glory - including the Spanish empire - was certainly a key element of Francoist ideology. Yet equally, such aspirations were always going to be tempered by reality. Francoist Spain, particularly in its early years, was poor and isolated, and could not hope to project itself across oceans even without considering the hostility of other powers. The United States, it can be readily assumed, would not tolerate direct Spanish intervention in its sphere of influence, which covered (from the Phillipines, to the Caribbean and Latin America) just about all of Spain's former colonies. Quite aside from Spain's utter inability to compete with US power, after the Second World War, Spain sought to align itself with the United States as an anti-communist ally. As such, whatever the rhetoric of Franco recovering Spain's past glories, there is no indication that reconquering these colonies was ever seriously considered.
Rather, Spanish imperial ambitions manifested themselves in Africa, particularly Morocco where Spain still retained some territory. The Second World War offered the prospect of Spanish expansion at the expense of France, who controlled most of North-West Africa. This was a key point of contention during negotiations with Germany about whether Spain would join the war in late 1940 - a key Spanish demand was territorial concessions in the region. This was a sticking point for Germany, for whom the loyalty and continued cooperation with their new Vichy client state was a higher priority. Spain attempted to directly negotiate with Vichy for concessions (unsuccessfully) up to 1942, when the Torch landings rendering the question moot. In the end, Spain did not manage to expand its territory at all during the war, and any remaining illusions of Spanish imperial glory were shattered when France granted independence to Morocco in 1956 - Spain quietly followed suit a month later, well aware that their position in the region was untenable.
It is worth noting though that Francoist Spain did not ignore Latin America. Instead of pursuing what would have been an utterly delusional policy of re-establishing their American empire, Franco instead set about rebuilding Spanish diplomatic, cultural and economic influence in the region. This was built on the concept of 'Hispanidad', projecting the cultural ties and unity between Spain and its former colonies, emphasising the ties of a common language, history art and architecture - as well as Catholicism and anti-communism. This policy achieved limited success in building direct economic and political influence for Spain - even after the Spanish economic recovery in the 1950s and 1960s, there was no way for Spain to compete with American economic power in the region. It did however make some diplomatic and cultural progress, and indeed has been continued in some ways since the restoration of Spanish democracy through institutions such as the Organization of Ibero-American States.