Frankie is a nickname, so it's hard to make a nickname out of it. Unless it's Fran, maybe.
Famous people named Frankie:
Actor Frankie Muniz; singers Frankie Valli, Frankie Avalon, and Frankie Laine; YouTuber (and brother of Ariana Grande) Frankie Grande.
The most famous Frankies at the moment are male, but the name has recently become popular for girls too; actresses Amanda Peet, Drew Barrymore, Sarah Chalke, and Bridget Regan all have daughters named Frankie.