A person with a felony could probably start a non-profit organization. However, if there were to require certain funding or loans their felony status might cause a problem in securing the funding. Also, depending on what the non-profit organization is certain persons might not be able to be engaged in that specific organization if there felony was related to it. In other words, if they had an offense against children they obviously would not be able to be in an organization that had children around them. Generally, there would not be anything preventing them from starting a non-profit organization but I would suggest checking your state laws.
