Radio Interference

if it is fuzzy, as in losing the station, it is probably a radiated RF from the flasher causing the radio to drift. Probably move the flasher unit farther from the radio and don't allow the case of the flasher to touch metal if it has a metal body.
If it is fuzzy, as in pops and whistles, shrieks and static, it is probably a grounding issue or a back feed interference issue with the flasher. Without the specifications on the flasher and a real wiring diagram I cant suggest a filter but there are inexpensive power line filters that may work to decouple the noise on the power.
One way to tell is to closely watch the indicator light of the head unit while the turn signals are operating. If it pulses with the turn signals, probably a filter is required. If you can send me a wiring diagram I can look and suggest a cheap fix. part number and manufacturer of the flasher and turn signal led bulbs would help as well.