Since the raspberry pi zero takes less power to power up. How many AA batteries do I need to power it up to play a movie in a loop? And how long would this last?
I suggest not going with AAs but just getting a high mAh phone charger. I have one about the size of the PI that has 10,000 mAh. I used it all night and it didn't seem to go down any (of course it only has 3 bars so I'd guess it was still over 2/3 full). Easily recharged--and 2 or 3 of them will keep you going indefinitely.
I wouldn't suggest running directly off AAs at any rate--the voltages don't match up quite right (6v is a little high for 4xAA and 4.8 is a little low for 4xAA rechargeable).
I have seen USB phone chargers that take 4,6 or maybe 8 AA batteries, that might work but even with 8 I doubt you'd get more than the 10,000mAh rechargeable.