The damage you are showing is minor cosmetic damage.
If the following occurs with sidewall damage, then get it replaced:
- Tire deflation (cannot be legally repaired in most countries)
- You pull the flap back and see damage to the side wall plies (corded area under the rubber which supports the tire) whether deflation has occurred or not
- Bulging of the tire at the damage site
If you aren't seeing any of these things, you should not have any issues running your tire until the tread wears out (normal use).
As a side note (and primarily my opinion with nothing to really back it up), the area where your damage has occurred seems to be extra rubber put in place on low profile tires to help protect the rims from curb rash. Yours looks like it was a little more serious of a curb encounter, but still, if no issues as stated above, you should be fine.
EDIT: If the flap of rubber sticking out bothers you (aesthetically), use a small amount of rubber cement to it and it should keep it in place. It really isn't bothering anything the way it is.