As mentioned, the flatness of the fingerboard is determined by its radius. A larger radius is flatter.
The thickness of the neck, front to back, is often specified by the maker. For example, Ibanez specifies the thickness at the neck and the 12th fret.
The width of the neck, bass to treble, is also often specifies. Ibanez specifies at the nut and the last fret.
If you like your BTB 6-string, then I suggest a BTB 5-string. Their neck radius is 400 mm, and they are quite thin, front to back. If you also want the neck to be narrow, then I suggest the BTB33. It also has a 33-inch scale, and the bridge is far down on the body (by the strap button), as on the the 35-inch BTBs, so the reach is 2 inches shorter than the 35-inch BTBs and many 34-inches bases (where the neck is further from the end of the body). That might be good for arthritic hands.