Absolutely not and you should use the same manufacturer of the paint you have on there also. Sorry you can only use a chlorinated rubber base paint on a rubber base paint. If you try to paint with the chlorinated rubber base on top of a synthetic rubber base paint it will probably peel like a bad sunburn.

You can try using denatured alcohol if it was latex paint. But it is probably cheaper and easier to just replace the vinyl cove base.

According to Martha Stewart it takes at least thirty days

Yes, but if the rubber stretches, it will crack the paint.

When you say rubber base paint I assume you mean latex paint. Yes, latex paint will adhere to an existing epoxy finish. However, the epoxy must already have cured. Meaning, it was already applied sometime in the past. A pretty good rule of thumb to go by when you're unsure if two finishes are compatible is to apply a coat of primer. Also, when latex paint is applied to a primed surface it will last that much longer, appear more uniform and will usually require only one coat of paint for proper coverage.