As in Episode 1, Starz got the broad historical outline right in Episode 2. Henry did indeed leave Katherine behind as Regent and therefore Commander in Chief of his armies when he went to France to fight what became known as "The Battle of the Spurs." That battle was soon followed by the birth of their second son, who lived a few hours at most.
But Katherine was not present for the victory at the Battle of Flodden on the Scottish border, which was very different and much more modern than Starz portrayed. She did have an important role and something famous to say about it, however.
Understandably, Starz left out some details that might have made the storyline too complicated. Losing those details, though, made some events difficult to understand. And some of the minor characters are doing things they did not do in real life.
In fact, the Battle of Flodden had been anticipated by Henry, who had a standing army in the north, ready to repel a Scottish invasion and already under the commend of Thomas Howard. Katherine undoubtedly helped Wolsey with logistic details—supplies and the like—and may have had a part in organizing a second Midlands army under Thomas Lovell. Her involvement thus went far beyond what was expected of queens in that era—but not to the extent of donning armor and participating in the fighting.
The battle was not as portrayed, either. First, both sides had cannons—the atom bombs of that era—and the English were not wielding farm implements and pitchforks. They had their famous English longbows and something called a "bill," a kind of halberd that was superior to the medieval pikes wielded by the Scots. Contemporareous accounts give the English archers much of the credit for the victory, but Howard's superior skills as a tactician also played a part.
Flodden also involved huge numbers of men, for that time. Modern estimates put the English army at around 26.000 and the Scottish around 30,000. Casualties are estimated at 4.000 Engish dead and 10.000 Scots. Scotland not only lost its king, but most of its nobility.
Here's the famous story about Queen Katherine, after the battle of Flodden: when Howard brought her the King of Scotland's bloody cloak, she complained both to him and by letter to Henry that she should have been brought King James's head. She actually had his body brought back to England and kept embalmed and unburied in Sheen Priory, ostensibly because the Pope had excommunicated him for siding with the French. The English thought her quite bloodthirsty.
The diplomatic background to all this was also simplified by Starz. Essentially, most of Europe including the Pope was at war with Louis XII of France, who declared Edmund de la Pole the true king of England and gave Edmund's younger brother Richard a command in the French army. So Starz' explanation of the execution of Edmund de la Pole before Henry left for France was incomplete. Edmund was not a simple innocent, locked in the Tower. He was the man the French wanted to put on the English throne.
There are other oddities about Margaret Pole's family in this episode. Reginald Pole did indeed spend part of his childhood in a Carthusian monastery, among monks who were silent much though not all of the time. However, there is no historical evidence that he had trouble speaking or any reluctance to speak. (I realize Philippa Gregory treats Reginald that way, but the three biographies of Katherine and Henry I read, listed below, do not.) To the contrary, he started at Oxford the year before the events in Episode 2, graduated with a B.A. three years later, took another degree at Padua (the oldest and most famous university in Europe at the time) and became a renowned scholar and diplomat.
There is also no evidence that Thomas More was ever Reginald's tutor, or that More carried on a flirtation with Lady Margaret. More had been married for years and was educating his daughters, practicing law, serving as a Member of Parliament, and acting as one of the undersheriffs of London. Margaret, then, was impoverished. There is no possibility that More would have chosen to tutor her son.
As for Sir Charles Brandon—he undoubtedly flirted with Princess Mary, because he was a rake, and had known her since childhood. What goes unmentioned is that he has already had two wives and several children. However, by 1513 he was a widower.
Even though I know the history fairly well, I can't wait to see what happens next!
Recommended biographies of young Katherine and Henry (all a bit dull but serious history):
Hutchinson, Robert. Young Henry: The Rise of Henry VIII (St. Martin's Press 2011)
Williams, Patrick. Katherine of Aragon (Amberley Publishing 2009)
Fox, Julia. Sister Queens: the Tragic Lives of Katherine of Aragon and Juana Queen of Castile (Ballantine Books 2011).