Three books you need on your writing desk if you want to write flash fiction
Brevity by David Galef - A concise, easy to read introduction to the flash fiction format. Each chapter focuses on a different genre/format and includes representative stories and prompts.
Flash! by John DuFresne - Lots of great exercises to get flash fiction writers up and writing. Has the feel of being in a graduate level fiction writing seminar.
Flash Fiction America (or others in the Flash Fiction series) - There are several anthologies in the Flash Fiction series. Phenomenal examples of the form. Lots of inspiration to draw from.
Bonus:
The Rose Metal Press Field Guide to Writing Flash Fiction by Tara L. Masih - Fantastic resource that includes 20 plus essays specifically on the craft of flash fiction.