I would like to know how I would be able to implement pausing in my flash game?

Ideally your game is going to have one single game loop that controls all of the action - most flash gaming frameworks will provide this for you. Somewhere, something is listening for Event. ENTER_FRAME and running logic on each frame.

One way to alleviate the animation problem is to hide your game screen when the game is paused (open a "game paused" window over the main game screen), so you save yourself the bother of stopping all the animations. If you prefer stopping the animations, the simplest solution I can think of is registering all animating objects in an array, so you can stop them all and play them all again in a simple loop. Not elegant, but better than refactoring your game for a pause function.

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