An interesting idea. Here are some random thoughts, which certainly may be wrong since I have never tried this.
To use the same screen would require reversal processing of the black and white film, or reversal in software once scanned. To print on color negative paper (RA4) you would need a custom CMY screen that reverses the one used for taking. I don't know if those are available, but I doubt they are common if they are.
If you want to use this for movie film I think getting things in register at projection speed would be very difficult. You will also lose resolution, which may be important at the small 8mm size. If you make the screen course enough registration gets somewhat easier, but the resolution will go down more.
The screen on many digital cameras is very fine. It may be too fine for all but the finest grain films out there.
You will lose film speed with the filters. The ideal speed for each color may be different, so you may end up with a channel or two either over or under exposed. The film spectral sensitivity will play a big part in this. Some films may work better than other.
I imagine you could get a screen for 8mm by simply scavenging one from a busted low res DLSR. And of the APS sized ones with the low 6MP resolution should be cheap and plentiful. I would start with on older Nikon D100 / D70 or early Canon Rebel. I'm sure there are many others, and some of them sure to be sold cheap for parts on ebay. If you want to use it for larger film it will be much harder to find. You could also contact some of the companies that convert cameras to IR or monochrome and see if they have some they would sell for cheap.