Speaking as a ticklefag who loves all sorts of RPGs, I feel like I say this any time the subject comes up, but I hope it goes without saying: NEVER introduce your fetish into a regular game, no matter how sneaky and subtle you think you're being, it will always stand out like a sore thumb. Even if it's a druid who happens to be barefoot, the second you call out that she's barefoot someone's gonna clock you.
If you were to set up a game with other ticklefags,it could be fun, sure. But you'd have to make sure you're all on the same page. No two ticklefags are entirely the same and if you get a couple who are into the storytelling and roleplay and a couple who are just looking to masturbate at the table, everyone is upset. A tickle RPG would basically be a standard tickle roleplay but with some gameified elements. I know DnD is just the brand name standard and it's the surface level most people know, but I don't think it would be a great fit. I'd probably take a more rules-light and most importantly generic system so I could run people through whatever sick fantasies they all came to the table for.
I've been thinking about putting some time into a Cortex Prime or Genesys game based around tickling because those two books are very toolbox-y, but even something as simple as Fate would probably work really well. Fate lets you create aspects to your character that you can either spend points to use to your advantage or have used against you to get more points. I could see characters having a ticklish weak spot aspect that puts them in a bad situation if an enemy exploits it, and it lets you customize your abilities with stunts so you could write one that activates when you're tickling someone or being tickled. And past that pretty much all it is is rolling dice to see if you beat a target number. If you're looking for essentially a group tickle RP where there's a system in place to determine if you succeed or fail at something or what sort of twists occur in the narrative to put your characters in ticklish situations, Fate could work great. Also the rules are all free. So that helps.