Mine started making this exact noise from the rear at some point in the month after taking it off-roading that included a few mud puddles. At first I barely noticed it but it steadily got worse, to the point where you could hear every little flex of the suspension in the cab with the windows down. I had cleaned/sprayed off everything you could see from just standing next to the wheels but had never gotten down and looked from the underside - which looked like a mud bomb went off. Today I took it to the manual car wash and sprayed the leafs and all the connection points with soap and water, heavy on the rear section from underneath the bumper. Tons of muddy water came out and now the sound is completely gone (for now, hopefully for good).
Sorry to grave dig here, but I'm still experiencing a squeaky rear end. I have an 18 SCrew with 35,000 miles on it, fully stock.
Spraying the rear suspension components with water quieted things down for only a day or two. Since then I've tried spraying everything down a number of times, including twice jacking the rear from the tow hitch as high as I could get it with the stock jack and a a few blocks/boards (so quite a ways up but wheels not fully hanging), letting it air dry some, then blowing out the remaining water with the leaf blower. Each and every time the noise would go away and then come back within a few days and then steadily get worse as time goes on. Obviously, and for whatever reason, getting the suspension components wet temporarily helps.
I scheduled a service appointment with the local dealership and after waiting a month and a half was finally was able to get it in yesterday. They are still going over the truck and haven't given a definitive answer, but when I called just now for an update the advisor mentioned that he is aware of a TSB which claims the shocks on these model trucks do begin to squeak as they age, it's considered to be normal operation, and maybe it's that (he was also careful to say maybe it isn't).
I thought it was interesting that he mentioned the shocks and not the springs, as it sounds like it's coming from multiple places in the rear and on both sides (to my untrained ear). Anyway, I just wanted to gather thoughts from others (maybe @FordTechOne ?) to prepare myself for them to come back and tell me this is normal.
To reiterate, this truck has 35,000 miles and has been off-roaded some (at most 100 miles total) but is overwhelmingly a daily driver. Am I really to believe that driving down a nearly flat street should produce audible noise from the rear (from every little flex of the suspension) and I should wake my neighbors when I back out of the driveway (off a curb) or try and walk around the bed? Seems preposterous and frankly I am embarrassed to drive the truck as-is.
I am not trying to get out of anything that may be my responsibility here. If everything was super dirty and they clean it out, I am happy to pay for that service since it wasn't a failure/malfunction.