Can fields generated by an antenna damage an iPhone?
Depending on the power of the transmitter and the wavelengths involved, the probability of the transmission interfering with the cell phones ability to communicate with the tower or wifi or whatever is fairly high though not damagingly, especially if the phone is really close to the antenna. 

The probability of the transmission generating a damaging arc across some junction within the cell-phone is much much less, probably close to, but not zero. Distance also matters. A few inches or millimeters is much more likely to do damage than say six feet.

The risks are probably slight, but as such, why take the risk. When working in the vicinity of this stuff, unless you REALLY need to use your cell-phone in there, which you should not, leave it outside.