1) Is that a ball screw or acme screw going thru the box? And you want to rotate it at 4000 rpm? You didn't ask about this but I will comment anyway. Without some intermediate supports I think your screw (or shaft) will destroy itself at that speed from whiplash. I don't think you will ever get to 4000 rpm.
2) And, not asking you to reveal too much proprietary stuff here, but why the slip ring? Some electrical signals are going through there? Is the shaft hollow to allow conductors internally?
3) "I am trying to find what you mean by "flexible coupling" You already have one on the drive end. At least that's what it looks like between the motor and the shaft. You will need a flexible coupling on the slip ring only if it is hard mounted to some stationary surface. I would think you would want to mount it directly on the shaft and just restrict its rotation with some kind of flexible arm or strap. You need a flexible coupling whenever you have two hard-mounted and connected rotary devices. For example, the centerline of your shaft is determined by the position of your bearings. The position of the centerline of the motor is determined by its hard mount. You will do everything you can to get the motor centerline and shaft centerline exactly aligned. But it will never happen. Ever. That's why you need a flexible coupling. It transmits torque between two misaligned shafts.
4) Something better than wood? Aluminum. Maybe even plexiglas or lexan. Depends on how long this system should last and how much it will be used.