As Eddie Thawne mentioned in Season 1:
So everyone but Iris?
basically everybody and their mother knows the "Secret" Identity of The Flash (currently, since the question asks about how many people know, the answer - depending on your definition of alive and people - is 26-28 individuums know it, which increases to over 30 if you include already deceased people in the know):
Henry Allen, Joe West, Iris West (& Nora Allen, technically, for all the good that information did her)
- The Coworkers (of the family):
Eddie Thawne, Linda Park
Patty Spivot (who figured it out all on her own, and didn't actually get a real confirmation from anybody, but called The Flash by his real name under her breath with her last words, so she does indeed know, and would technically fit into the previous category)
- The (extended) Star Labs Crew:
Harrison Wells (Earth 1 & Earth 2), Cisco Ramon, Caitlin Snow, Ronnie Raimond, Jax Jackson, Dr. Martin Stein and his wife Clarissa Stein, Jay Garrick and the (maybe currently still locked up in the Pipeline, who knows really?) Henry Hewitt, Bette Sans Souci.
- The (extended) Team Arrow:
Oliver Queen, Felicity Smoak, John Diggle, Lyla Michaels, Roy Harper, Thea Queen, Laurel Lance
Lennard (Captain Cold) Snart, Malcolm "I'm Ra's al-Ghul" Merlyn, General Wade Eiling, Grodd (do Gorilla's count?), Clyde Mardon (he at least saw Flash without the mask, but didn't live long enough to tell anyone about it), Tony Woodward, Zoom.
Cold, Jax, Ray, Stein (again), Kendra "Hawkgirl" Saunders, Carter "Hawkman" Hall, most probably (being from the future, and having Gideon as his crewmate, but as of yet unconfirmed) Rip Hunter -- so basically all of them except Sara Lance and Mick Rory.