They do suggest a 10A supply as one possible choice - I presume the board will take 1A per servo
(perhaps getting warm in the process), otherwise it would be struggling to run 16 servos at all.
So long as you power supply can handle that sort of peak current it should all work - for 1.5V cells you'd
need some very big ones - a 6V SLA battery might be more practical (unless weight is an issue).