It depends what you mean by fluid -- Flash games typically use a vector art style with skeletal animations -- that is, you have a single "sprite" that's made up of many smaller, independent parts (head, body, upper and lower arms, upper and lower legs, hands and feet), and you animate the sprite mostly by posing all those parts in relation to one another -- kind of like a claymation model with a metal armature inside.
This kind of animation has a look that's fluid, but also tends to have a peculiar, almost mechanical look about it. Of course, it looks as good as your animation skills allow, but producing natural-looking animations in this way is not straight-forward.
Another kind of animation is to draw separate images for each frame of the various motions your characters can make. Its a lot of work, but the end results have a very different character than with skeletal animation.
The first step is to understand the requirements and ramifications of both of these approaches, both artistic and technical, and then to choose which style suits you. Then you can worry about how to begin production of the assets.