Here's what will be airing on FX and FXX on Father's Day, all times Eastern-

FX:

7am-According to Jim: "Period Peace" (S7E7, OAD: February 12, 2008)
7:30am-According to Jim: "The Rendezvous" (S7E8, OAD: February 19, 2008)
8am-Miracle (RD: February 6, 2004)
11am-Thor (RD: May 6, 2011)
1:30pm-Thor: The Dark World (RD: November 8, 2013)
4pm-The Avengers (RD: May 4, 2012)
7pm-Avengers: Endgame (RD: April 26, 2019)
11pm-Ford v Ferrari (RD: November 15, 2019)
2:30am-According to Jim: "Goodwill Hunting" (S7E9, OAD: February 26, 2008)

FXX:

7am-King of the Hill: "Hank's Got the Willies" (S1E4, OAD: February 9, 1997)
7:30am-King of the Hill: "Shins of the Father" (S1E8, OAD: March 23, 1997)
8am-King of the Hill: "How to Fire a Rifle Without Really Trying" (S2E1, OAD: September 21, 1997)
8:30am-King of the Hill: "Next of Shin" (S3E5, OAD: November 3, 1998)
9am-King of the Hill: "Good Hill Hunting" (S3E8, OAD: December 1, 1998)
9:30am-King of the Hill: "Chasing Bobby" (S5E9, OAD: January 21, 2001)
10am-King of the Hill: "Yankee Hankee" (S5E10, OAD: February 4, 2001)
10:30am-King of the Hill: "Of Mice and Little Green Men" (S6E14, OAD: April 7, 2002)
11am-King of the Hill: "My Own Private Rodeo" (S6E18, OAD: April 28, 2002)
11:30am-King of the Hill: "Returning Japanese (Part 1)" (S6E21, OAD: May 12, 2002)
12pm-King of the Hill: "Returning Japanese (Part 2)" (S6E22, OAD: May 12, 2002)
12:30pm-King of the Hill: "It Came from the Garage" (S12E21, OAD: May 11, 2008)
1pm-The Simpsons: "Like Father, Like Clown" (S3E6, OAD: October 24, 1991)
1:30pm-The Simpsons: "Burns, Baby Burns" (S8E4, OAD: November 17, 1996)
2pm-The Simpsons: "Insane Clown Poppy" (S12E3, OAD: November 12, 2000)
2:30pm-The Simpsons: "The Dad Who Knew Too Little" (S14E8, OAD: January 12, 2003)
3pm-The Simpsons: "Fat Man and Little Boy" (S16E5, OAD: December 12, 2004)
3:30pm-The Simpsons: "Father Knows Worst" (S20E18, OAD: April 26, 2009)
4pm-The Simpsons: "Dad Behavior" (S28E8, OAD: November 20, 2016)
4:30pm-The Simpsons: "Daddicus Finch" (S30E9, OAD: December 2, 2018)
5pm-Bob's Burgers: "Sheesh! Cab, Bob?" (S1E6, OAD: March 6, 2011)
5:30pm-Bob's Burgers: "Spaghetti Western and Meatballs" (S1E9, OAD: March 27, 2011)
6pm-Bob's Burgers: "Best Burger" (S5E5, OAD: November 30, 2014)
6:30pm-Bob's Burgers: "Father of the Bob" (S5E6, OAD: December 7, 2014)
7pm-Bob's Burgers: "L'il Hard Dad" (S5E14, OAD: March 8, 2015)
7:30pm-Bob's Burgers: "Hawk & Chick" (S5E20, OAD: May 17, 2015)
8pm-Bob's Burgers: "Motor, She Boat" (S10E3, OAD: October 13, 2019)
8:30pm-Bob's Burgers: "Poops!... I Didn't Do It Again" (S10E20, OAD: May 3, 2020)
9pm-The Simpsons: "Saturdays of Thunder" (S3E9, OAD: November 14, 1991)
9:30pm-The Simpsons: "Homer the Father" (S22E12, OAD: January 23, 2011)
10pm-Family Guy: "Peter's Two Dads" (S5E10, OAD: February 11, 2007)
10:30pm-Family Guy: "The Former Life of Brian" (S6E11, OAD: April 27, 2008)
11pm-Family Guy: "Brian's a Bad Father" (S12E11, OAD: January 26, 2014)
11:30pm-Family Guy: "Quagmire's Dad" (S8E19, OAD: May 9, 2010)
12am-Futurama: "Hell Is Other Robots" (S1E9, OAD: May 18, 1999)
12:30am-Futurama: "A Flight to Remember" (S2E1, OAD: September 26, 1999)
1am-Futurama: "Mars University" (S2E2, OAD: October 3, 1999)
1:30am-Futurama: "When Aliens Attack" (S2E3, OAD: November 7, 1999)
2am-Futurama: "Fry and the Slurm Factory" (S2E4, OAD: November 14, 1999)
2:30am-Futurama: "I Second That Emotion" (S2E5, OAD: November 21, 1999)
3am-Futurama: "Brannigan, Begin Again" (S2E6, OAD: November 28, 1999)
3:30am-Futurama: "A Head in the Polls" (S2E7, OAD: December 12, 1999)