RE: Warning Chime with turn signal
If the dealer INSTALLED the flatbed, as you stated, it's their problem. Just because you chose to have a flatbed put on by them, doesn't relieve them of the responsibility of a proper and correct install.
Take it back.
It sounds like a power wire backfeeding into the system, due to improper installtion somewhere. Aftermarket bodies should also have a separate ground to the frame, and not reply on the metal to metal contact of the body and the frame or U-bolts that hold the body on.
A circuit searching for a ground can cause funky issues as well.