You’re right, I don’t have much knowledge of anarchism’s philosophical framework, but I do know that the definition of the word means that there is no authority.
In an anarchist society, what’s to stop me from accumulating wealth?
Furthermore, what would stop me from entering into voluntary contracts with others who agree to do labour in exchange for money?
Ultimately I think that without some authority (almost certainly a state) enforcing communism, the relationships we currently experience under capitalism will naturally reoccur. And (if my limited understanding of anarchy is correct, which I admit it might not be), under anarchism there can be no such authority preventing capitalism from happening.
Communism always needs to be enforced, it doesn’t happen naturally. Capitalism does. That’s why I don’t think communism can exist along with anarchy.