Were there flying dinosaurs in the permian period?

No. There were no dinosaurs in the Permian period. The first dinosaurs appeared about halfway into the next period: the Triassic. Pterosaurs, flying reptiles that are often incorrectly called dinosaurs appeared a few million years after that. Birds, which are true flying dinosaurs, first appeared in the late Jurassic period. The only flying animals in the Permian were insects.