The trick, if you don't want to plop down the money just for the program, is to take a class at a local community college or something that has it in the computer labs.
In any case, given that you're talking about a pretty big effort there, you may save time even if you include working to get the cash to buy it. It's a lot faster to animate in than Paint, but it does require some time/effort to learn.
Example Flash animation: Nightmare City
and Nightmare City -Catastrophe-