This mob has since been moved from Biomes O' Plenty to the mod Familiar Fauna,a mod created by the same development team.
Dragonflies can be caught using Bug Nets and Bug Habitats. If you have an empty Bug Habitat in your inventory, the dragonfly will automatically be placed in it when caught.
Additionally, dragonflies named using Name Tags will retain their name even when caught and placed in a Bug Habitat. The name will stay if you release them as well.