Is flyer distribution considered soliciting?

No, its not solicitation per say. . your cousin is doing a job. Usually housing developments don't like these flyer's because people sometimes throw it all over the place and they end up cleaning which cost them money. Yes they have a right to stop you leaving flyer's in their property. however flyer's sent through US Post is delivered to the individual addresses. Same way there are tons of flyer's in the weekend news papers.