Good Sam (ugh, I know...) puts out a "Dinghy guide" each year. That's where I would start. They put vehicles in that guide that have "dinghy tow" (AKA flat-tow, four-down, RV tow...) instructions in the owner's manual. So it's not an exhaustive list of everything that can be flat-towed, but it's definitely a great place to start. Find a few options, and look up the manuals on them, and read the instructions to see if it's something you're willing to undertake. Some vehicles are easier than others, and what may look "reasonable" in the manual can become a serious PITA when you're out there doing it...
For example, my wife's Yukon Denali is technically flat-towable, but you must disconnect the battery while in tow, and the process for flat-tow prep is a bit cumbersome IMO. I'm just not willing to do that given that we tow my Jeep (which is super easy). If we had the Yukon first, and it happened to be our only available toad, I might consider setting it up though. But the other consideration is that's a lot of truck to be towing behind the camper...
I have towed a Jeep YJ (Stoopid simple), a Grand Cherokee (WK2), and now my Wrangler JLU. None of them are/were dedicated dinghys, they have been my daily driver, and that's one of the reasons they were chosen (except the YJ, but it's a "Sunday fair-weather toy). They are all simple to tow IMO, but I turn all my own wrenches, so I'm intimately familiar with how it's done and why. I also use my JLU to get around off-road, and tow a small utility trailer or my small aluminum boat. IMO, it's a fantastic vehicle for my needs outside of use as a dinghy. Any toad has to handle multiple duties in my house; I absolutely loathe "one trick ponies". I'd rather tow the Yukon than purchase another vehicle specifically for a dinghy.
In the dinghy guide, they usually also give a brief summary of the basics of dinghy towing, what you'll need, and review a couple different items from each category of gear. And everyone has their own opinion of what makes a good dinghy, and what their threshold is for level of difficulty.