My 5c can take pictures as rapidly as I can hit the button. On iOS 8.0.2.
In fact, I can take pictures faster on the 5c by hitting the button repeatedly than I can holding it down! (Since the 5c doesn't have the official "burst" mode.)
2.4 fps constant in "hold down" mode, up to 10 fps intermittent in "tap the on-screen button as fast as I can" mode. (A couple different tests of "tap as fast as I can" produced different results. One managed to hold ~10 fps for 10 seconds. Another run managed 10 fps for a few seconds, then 'paused' (while writing the pictures out, presumably,) for a second or two, then 10 fps for a while, then paused, etc.)
Just tested with the volume button triggering, clicking as fast as I could, and got about 6 fps.
(All were calculated by using a stopwatch, starting as I started to take pictures, and taking pictures for 10 seconds. Then dividing the number of photos taken by 10 to figure fps.)