Well we know that Katherine will eventually miscarry this son...
Unless butterflies cause the child to live. Do we know what the cause of the miscarriage was?
Yeah, Katherine miscarrying her child is not a forgone conclusion.
Nope, we can guess (stress, her shitty fasting habits, Henry's sperm had problems with it), but we do not know for sure
If the son survives and doesn't pull a Henry, Duke of Cornwall then we will have Katherine following onto the footsteps of her grandmother-in-law, Margaret Beaufort, and she would do her best to ensure her son is devout Catholic and pair him off with one of her nieces (perhaps a surviving Infanta Maria of Portugal, b. 1513)
If the boy survives Katherine will go through heaven and earth to make sure that he rules and keeps his throne. Maria would be a great match for the boy, as would Reneé of France and maybe one of his Danish relatives.
If the child doesn't survive, I suppose this means an earlier Union of the Crowns? If James IV still dies at Flodden, would James V end up being raised by Margaret in England, or would Margaret rule from Scotland until James' regency ends? If James IV lives, then James + Margaret = British Catholic Monarchs.
It would likely result in an earlier union of the crowns, though it’d be interesting to see where James is raised and who Margaret remarries too. It would cause a whole lot of drama.
Probably, what else is there for her in England?
She could possibly remarry but that's unlikely
Charles of Savoy, perhaps, as the third husband?
Charles of Savoy is the most likely third husband for Katherine, with, Louis XII being a close contender.
Pulling a Henry, Duke of Cornwall is probably the way for maximum chaos- everyone anxiously waits to see how Catherine's pregnancy ends up, then she births a healthy son, everyone starts settling in for a regency... and then a few months later the child dies and everyone has to start scrambling again.
That would be quite chaotic. After the son dies, Katherine would probably have an “alright I’m out” moment while the country begins to tear itself apart.
Buckingham is also floating around.
Richard de la Pole was supposedly gearing up to invade England with some mercenaries in 1514 IOTL before peace intervened. Would France still be interested in backing him here, or would they be content with England being neutralised by domestic turmoil/a regency/female rule?
Buckingham would be a good alternative, he has a decent claim and could always have his son married to Mary Tudor or a daughter of Margaret to secure his dynasty’s legitimacy. Richard de la Pole is also a likely contender since the French would like an ally of their’s on the throne and a long civil war would prevent England from attacking France for a while.
Mary Tudor (the Elder) is also still present in England (and unmarried) at this point, so intrigue could surround her- maybe could be a bit of a focus for those opposed to union with Scotland? If nothing else, should one of the domestic male claimants make a play a marriage to her could be used to shore up their legitimacy (the eldest sons of both Buckingham and Devon are unmarried).
That is possible, especially since it strengthens all parties’s claims.
England JUST went through a civil war trying to find a king. Now that there IS a king, they're not going to start fighting again. Plus, Flodden probably isn't going to happen, what with the English king being dead and all...
Henry VIII had nothing to do with the flodden claim AIUI. It would likely still go ahead since someone needs to protect England from the Scots.