No, you can only earn the miles for any given flight in one program - a standard rule in the T&Cs of the FFPs.

However this need not be the same program that you get miles for payment of the ticket through an affiliated credit card.

These do not have to be the program of the airline flown, which is a major advantage of airline alliance.

Eg I could be flying Air NZ but credit miles (for flying) to Aeroplan (Air Canada FFP) and the ticket was purchased on Amex which I transferred miles (for spending) to say Qantas. But I cannot also credit miles to say Airpoints (Air NZ FFP) as they are already credited to Aeroplan.

If you try crediting miles for the same flight to multiple programs, and get caught, you could lose membership of those programs and forfeit all mileage balance, status, etc. Not worth risking IMHO.