How many degrees can you flex an arm of a lego minifig?
Within the shoulder socket, a minifigure's arm has full 360&deg; rotation, however the hand needs to positioned correctly to allow it pass the head, and it puts some strain on the joint:



Note that most accessories will block this rotation.

As the arms are made of the same ABS as standard LEGO bricks they aren't flexible, and so without heating (and permanently changing them) they don't bend or flex.