Red and black (lacquer) was a big deco color combination: I found a few things doing a google image search for "deco dresser" and so on:

You could do black with another color also; I've seen deco furniture with lavender and black, for example. I'm envisioning the furniture as shiny black, with shiny red/other color as the inside and outside scallop-area on the armoire and dresser. Also, I agree about replacing the knobs. Just make sure they are the same size or you will have to drill new holes.
Since a lot of deco furniture features patterns made with inlaid wood, another option might be to paint the different sections to look like inlay:

I know I've seen tutorials on how to do this, but can't think of anything. That would be more work than I personally want to do, but it might look cool.
From the picture, it looked like the furniture might not be solid wood, in which case you'd have to primer it before painting or the paint won't stick. Sounds obvious, but my mother, queen of the half-assed, tried to paint over fake wood paneling once...
Contact paper is one option, but I think paint would be easier (no cutting), more attractive and longer lasting in the end. However, there might be attractive wood-grained contact paper now that would replicate the inlay look. I just went to Con-Tact's website and they have the following:

Available in other fake wood patterns/colors also. You could trace the shapes and cut them out at a diagonal. However, I don't know about doing the tops/side of the dresser and armoire in contact paper... Again, I think two-tone paint would be the easiest and least complicated.