Standard anechoic chambers cover the walls with uneven foam structures, to disperse sound waves. The idea is that the soft foam absorbs most of the pressure waves, and the rest that is reflected, is reflected in different directions. If I've understood correctly, it can be difficult to place the foam structures without causing "resonances", where some frequencies are not dampened as much as others, because of how they happen to bounce between the foam structures in opposing walls; that it is a bit of a hand-crafted art to make anechoic chambers. Place foam, measure, replace, measure, etc.
I could have understood wrong, though; I've never made any anechoic chambers myself.
Personally, I would make the chamber ellipse-shaped (as viewed from top), with the equipment to be measured placed in one focal point, and a cylinder of fuzz at the other focal point, and cover the walls with standard sound-absorbing pyramid foam.
In an ellipse, all sound generated at one focus will reflect to the other focus. (There are buildings that use this as an acoustic effect; a whisper in one focus can be heard in the other focus, even if the distance is much greater than one would think a whisper could carry.)
The cylinder of fuzz is basically an omnidirectional sound absorber. Whatever sound it reflects, will be reflected back to the device, so the cylinder of fuzz would need to be as absorbent as possible. I'm thinking of something like a 4" diameter foam cylinder covered with a thick shag carpet.
The microphone would be placed at exactly 1m away from the equipment, as per standard. Actually, I'd use several microphones, so that the directionality of the noise could also be analyzed. If the equipment is typically used on a table, it would be on a table in the measurement chamber too. If handheld, then on a thin pedestal at roughly 1m height.
Essentially, instead of trying to make the walls uneven, I'd be assuming the opposite, and focusing the sound reflections to a dedicated dampener. Whatever covers the walls will hopefully absorb most of the acoustic energy, but some of it will always reflect. Having those reflections meet at a dedicated dampener, from which they're reflected back to the walls, should – I think and hope! – yield maximum damping, without relying on the small-scale structures in the walls dispersing the sound. In a way, such an anechoic chamber would have only one "really quiet spot", but that should be fine for measuring noise generated by equipment.