Flash CC Multiple Area Fill?

This is a really bad idea: Animate CC is (mainly) meant for vector animation, and pixel art is just not part of its feature set. Drawing squares like that is crazy and awkward.

If you want to incorporate pixel art in an Animate CC animation, use a proper tool like Pro Motion (meant for pixel art creation) and import the resulting bitmaps in Animate CC. Transform as needed. Or use Photoshop to draw the pixel art. ANY bitmap tool will do, really. Even Paint! But not Animate CC. Wrong app.

Any shapes that are currently selected will get changed to the fill color when you use the paint bucket.

There is a different need that you might have, where you want to later on change your mind about the color used in a whole lot of places, some of which might not even be on the stage at the time. In the Swatch palette is a Tag Swatch feature. You can convert any color to be a tagged swatch, and it will appear in a tagged swatches area. If you later double click on that you can change its color, and everywhere that color was used will get changed, without needing to use the paint bucket.