Does A K flush beat an A Q flush or is it a split pot?

The first one, for instance A-K-Q-J-2 will beat another suit of A-K-Q-10-9 because you disregard highest ties until you find whose highest untied card is higher.

Same thing, with, for instance, straights. A 2-3-4-5-6 straight beats an A-2-3-4-5 straight etc.

If you're playing Texas Hold-em, or another variant where you have more than 5 cards in play per person, only the best 5 cards are evaluated, so if the common cards showing are A-A-A-A-K, then it doesn't matter what other "extra" cards a player has. In cases like those, you'll split the pot.