My brother has Medicare and Medicaid. If a Dr takes Medicare, but is not enrolled with Medicaid, is the Dr allowed to charge the patient?

No doctor or clinic accepts cash because they have no way to process it into their bookkeeping system. If you try to pay out-of-pocket (like with a credit card) outside of Medicare, it will be prohibitively expensive.

When you call to make a medical appointment for your brother, you need to first ask if they accept Medicaid patients. In my experience, most doctors/clinics do not.

No, he cannot pay a doctor out of pocket. He has Medicaid because he has no money for doctors. And you cannot pay for him. You should have a Medicaid provider. You can call them to see what doctors take Medicaid. I found that Hospital groups usually have the doctors my nephew needs and they take Medicaid. Doctors are not allowed to except money from Medicaid recipients if they don't take Medicaid. This is how it was explained to me by one of my nephews doctors.

I would ask for a referral to someone who also accepts Medicaid. If he qualifies for Medicaid he doesn't have enough money to be paying gor a lot of copays. How about a dual coverage Medicare Advantage insurance? Check with your Area Agency on Aging or the state insurance commissioners office for where to get advice.
If a doctor is owed money why wouldn't their office take cash?