Hey, for the OP, here's the list of teams that made up the Federal League from 1913-1915. It might be used to look at what cards of what Federal League teams did show up in the Cracker Jack, T214, and T216 sets. There could maybe be a case where only one card for a particular Federal League team was ever issued among these different sets. That would certainly seem to make that team's card a possible candidate to answer the OP's question.
Teams........................Seasons.....Comment
Baltimore Terrapins......1914–15
Brooklyn Tip-Tops........1914–15
Buffalo Blues...............1914–15....Initially known as the Buffeds
Chicago Whales...........1913–15.....Initially known as the Federals or Keeleys
Cleveland Green Sox....1913
Covington Blue Sox......1913..........Also known as the Colonels. Transferred to Kansas City, mid-season 1913
Indianapolis Hoosiers....1913–14.....Moved to Newark in 1915
Kansas City Packers......1913–15.....Had been in Covington until mid-season 1913
Newark Peppers...........1915...........Moved from Indianapolis following the 1914 season
Pittsburgh Rebels.........1913–15.....Known as the Filipinos in 1913, and initially as the Stogies in 1914
St. Louis Terriers....... ..1913–15
After coming across some more info regarding Federal League teams on baseball cards, from SABR's site, looks like one of the Federal League teams may not be the answer to the OP's question after all. The article also mentions heretofore unnamed other sets that Federal League team players were included in.
https://sabr.org/research/article/fe...aseball-cards/