Simple Answer: Generally speaking, multiple flashing cannot damage the phone
Complicated Answer: All a flash does is reprogram the phone's memory. As you likely know, memory is nothing more than changing a bunch of electrons to an on or off state (i.e. a 1 or a 0). Flash memory can be written and re-written a hell of a lot of times before it starts to see deterimental effects.
The chefs themselves have stated that they generally flash multiple times and day with little to no ill effect. Nevertheless, if your phone starts to "die" after mutiple flashing, it is likely due to a hardware issue as opposed to being directly related to excessive flashing. And since hardware problems are covered under warranty, just bring it into the store and they should replace it anyway
So flash away