Communism is flawed because it is philosophically impossible. Man is mortal, not omniscient, imperfect and has free will. Communism aims to satisfy two things: Carrying an economic system by man's guidance and striving for compassion for all of it's participants in the process.
Are we to yoke the imperfect man who may at times choose to be compassionate and at other times not, with the task of knowing all the needs of the people in all aspects of their life and have the ability to run the State without error in such a selfless manner as to provide for all the needs of the nation?
To believe so is foolish arrogance.
To believe that such a system can be stateless is either blissfully or willfully ignorant of the historical truth that social hierarchy (and for that matter, private ownership) existed even in prehistory and clung to any existence of society and government to this date. Our understanding of society inextricably involves hierarchy.
I say this as someone who at a time had full faith in Communism over every other system.