First off....the Screen wall is inconsequential as far as any worry about reflections from the PJ is concerned. It can be any color as long as it is pleasing to your idea of Theater decor.
However, be advised that any Fire color (Red) or Brown (...will reflect a Reddish or Yellowish cast...) are not really great choices.
Flat Black is just plain "Pug-Ugly" and represents Old-world" thinking. And despite what most every uninitiated enthusiast thinks, it DOES
reflect quite a bit of light, and that being predominately "Blue". But in truth it reflects plenty of light....just not "as much as" a Matte White.
In the images as seen below, the first shows a Flat Black Painted (sprayed) Ceiling. Without much light in the room, nor any projected light illuminating the screen, yes...it looks pretty darn Black.
But....turn on the PJ, and even when appreciable ambient light is in play, the Ceiling is gonna reflect light like crazy. Even the Sconces' light Brown incandescent umbras cast a lot of light that is reflective.
Granted, the screen in use is one that does cast light equally in all directions, so the ceiling is getting washed pretty good, but that's why I chose that example.
Furthermore, a Matte / Flat Black is a dusty, cheap-looking affair. I strongly suggest you totally dismiss it from consideration. But if you simply have your mind set on such, then use a ultra Deep Black such as Disney's Mouse Ears, mixed into a Satin Interior Enamel, and absolutely have it sprayed on...not rolled.
Deep Grays, Dark Blues, Dark Blue Greens, most any "Cool Matte" Interior Enamel will do.
I personally like a Dark Blue Green Wall with a deep Dark Slate Gray ceiling.
The Color scheme should follow these dictates.
Mid-tone to Dark toned Wall Color in a Flat Enamel
Ceiling can be a Complementing "Darker" Color, or the same Color as the Walls only 3-4 shades darker
Trim should match the ceiling Color, only it should be a Satin Enamel.
Carpet should be non-reflective.