There are lots of metal on metal connections on a Road King and most are subject to flexing and vibration. In looking for a dry squeak (chirp) on mine I removed all of the crash bars, smeared a thin coating of anti seize on the contacting metal faces, but not on the bolt threads that I didn't want to vibrate loose, and put it all back together. In your case, the fitting at the top of the engine where the link from the frame joins the engine might be a good candidate for the thin smear of anti seize where the metal of the bracket touches the engine. Then there is the big sliding fitting on the head pipe which holds the flare against the exhaust port, smear a little anti-seize on the flare where it contacts the piece that bolts to the studs in the cylinder, both the front and rear pipes. Then there is a fitting clamping the rear head pipe to to the frame above the starter. Each of those metal to metal contacts might chirp. Have you pulled the mufflers up and down and side to side to see if the rubber supports are squeaking? Then there are the joints at the front of the mufflers to the head pipes and those clamps, all of which might squeak. The clamps holding the chrome heat shields around the exhaust pipes are subject to large heat variations, from ambient when cold up to 300 degrees plus each time the engine is run and they will loosen over time, snug all of those. Check to see if any of the heat shields are contacting another heat shield where they come together. Any contact points are subject to dry squeaks. See if your foot boards squeak when the weight on them varies. Booth the pivot shaft and the pads that provide the down stop can squeak. Passenger foot boards can squeak the same way the front ones might. I also had to smear some anti seize on the front fender mounting points to get rid of a dry crack that happened when firmly applying the front brake or when going over a significant bump. Front and rear fender trim are possibilities also. When you can hear the noise, grab the front fender front chrome trim and then the lower skirt and see if the sound changes or stops. Same for rear fender trim, tail light mount, license plate mount and license plate and saddle bag supports. Any of the rubber cushions on the saddle bag supports and mounts might squeak when flexing. The saddle bag support tubes, front and rear can be disassembled, lubed and put back together. Have you held foot pressure on the forward shift shaft with the heal and toe levers on it? Have you checked the shift linkage for any loose or dry parts? Paste silicone lube is good for all of the rubber parts mentioned so far. There are rubber pads on the bottom of the seat and seat/frame contact points which also would benefit from a thin smear of silicone paste. The handle bar risers have rubber cushions also but I would try everywhere else before getting into those. Good luck, if anything else pops into my memory I'll get back with it.
