You still have to go through some steps, but you can save yourself from having to paint the colors on in a tedious way.
Here a little explanatory video:
It's with your words, "flood filling" all black first, then selecting only the faces you want red and setting their color as well.
Change to Vertex Paint mode and in activate paint mode, to select the color black.
Make sure the object is completely selected by pressing A.
Then go under the menu "Paint" and use "Set Vertex Colors" (shortcut Shift+K) to fill the entire object with black color, this will also generate a vertex color group for you.
Now before you do anything, change the color to the red you want to use later.
Changing in the selection mode, mark the faces to be turned red and either use the menu or the shortcut Shift+K again. The selected faces should now be red while the rest is still black.