Make-up air certainly has to be taken from a clean air source. Generally, one wants to take air at least 10 ft from any exhaust air (or DWV vents) and upwind of them (relative to prevailing winds). There is no functional requirement on duct diameter or length, so long as the overall MUA system (which may include a blower and a filter and a heater) delivers sufficient air to the kitchen that the house internal pressure is close to the exterior air pressure. How close that has to be is determined by the presence of combustion appliances that might be back-drafted, as well as avoiding pulling air through wall leakage. There may be a local code requirement that the duct be at least the diameter of the hood duct.

Please review the many MUA threads here for more insight.

Usually, a blower-less MUA system (denoted a passive system), if it can be used, will use a very large duct, while a blower-based MUA system (denoted an active system) likely will be able to use ducting of the order of the hood exhaust ducting diameter.

Lacking, one hopes, any grease build-up, MUA duct can be any practical duct material, but steel or aluminum would seem to be best from a stiffness to weight perspective. PVC is also a possibility, but in large sizes may not be cost effective, and unduly heavy. Corregated duct will have higher pressure loss and increased noise.

Thanks for your reply. How far should it be from an air conditioning unit?

MUA is drawing in outside "fresh" air, and should have no incompatibility that I can see with an air conditioner. Of course, pulling in air from the hot side of the compressor will likely not improve conditions in the kitchen in summer. Also, adequate working room around each should be present.