After a couple visits to our local mechanics for brakes repair of a 2006 chevy siverado short bed reg cab. My rear brakes are the problem first the mechanics changed them out with premium pad then now dealers pads . After all that the squeaking is still going on . What might be the next step for helping my mechanics in fixing the problem completly ?

Make sure the mechanic checked the park brake shoes inside the rear rotors, they quite often break away from the lining and get wedged in the rotor, sometimes causing a constant squeal noise. I've also seen the brake pad anti-rattle metal clips become loose and wander in the caliper bracket, they lightly rub against the rotor and cause a squealing noise similar to worn brake pads. They are also very bad for the backing plates rusting out prematurely and rubbing on the inside of the rotor. Other than that he can just try to champher the edges of both front and rear pads to help dissipate the brake dust, from collecting and causing squeak noises.