The move itself should not take long at all, it depends more upon the number of users ahead of you in the queue to be moved.

After you’ve opted to move to another service, you’ll be added to a move queue managed by that service. The queue will be managed on a first come, first served basis. When they get to your Yahoo! Photos account, they will copy your original resolution photos into the account you identified on their service and send you an email when the move is complete.