Like DE_Glide mentioned, that amp is a Class D amp and will mess with your reception. It is a very common issue among most motorcycle amps, especially the Hogtunes. An internal fairing antenna is NOT going to help with reception (that would only make it worse), but you could try moving the grounding point to see if that helps. If it does, it won't help much unfortunately.
There are only a few motorcycle amps out there that won't mess with your reception (Biketronics amps and Arc Moto 600.4 for example). Not wanting to loose FM was a necessity for me, and thus why I ended up going with Biketronics. Their amazing customer service and lifetime warranty are pretty awesome too.
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'15 FLTRXS - V&H Power Duals w/ Screamin' Eagle Street Cannons - Arlen Ness Big Sucker - BT4180.14 w/Arc Moto 602v2 and Polk MM652 - Le Pera Maverick Daddy Long Legs - Advan Lowers - Freedom Shield 15"