I realize this thread is months old, but I'm bored.
I did an hour radio show on food songs once. It was cheezy, but fun. I won'l make a lindy hop distinction (as was the intent of the original request) for you here because many of the songs are in the 40's R&B vein. Some of these I wouldn't play at a dance either

And finally, I'm sure I missed a ton, but this was just from skimming through my collection.
Cab Calloway (or any neo swing band.. ha!): Everybody Eats when they Come to My House
Cab Calloway: Pickin' Up The Cabbage
Benny Goodman/Charlie Christian: Breakfast Feud
Dinah Shore: Shoo Fly Pie and Apple Pan Dowdy
Eddie Condon: Home Cooking
Benny Carter: Fish Fry
Erskine Hawkins: Corn Bread
Fats Waller: Eep, Ipe, Wanna Piece Of Pie
Fats Waller: Shortin' Bread
Fats Waller: All the Meat And No Potatoes
Jay McShann: Hot Biscuits
Jonah Jones: Struttin' With Some Barbecue
Les Brown: Tangerine
Louis Armstrong: Cornet Chop Suey
Louis Armstrong: Big Butter and Egg Man From the West
Roy Eldridge: Fish Market
Sidney Bechet: Hold Tight(Want Some Seafood Mama)
Will Bradley: Celery Stalks At Midnight
Will Bradley: All THe Meat and No Potatoes
Will Bradley: Fry Me Cookie, WIth a Can Of Lard
Will Bradley: Chicken Gumboogie
Muggsy Spanier's Ragtimers: Big Butter And Egg Man [this is a better version]
Rudy Greene & His Orch: Buzzard Pie
Lous Jordan (or any neo...): Saturday Night Fish Fry
Jesse Stone (or Louis Jordan): Cole Slaw (Same song as instrumental Sorghum Switch by Jimmie Dorsey)
John Brim - Ice Cream Man (blues)
Price, Sam & His Texas Bluesicians - Rib Joint
Hal Singer - Beefstew
Tiny Grimes Orch. - Boogie Woogie Barbecue
Joe Houston: Cornbread and Cabbage Greens
Louis Jordan: Beans And Cornbread
Louis Jordan: Onion
Louis Jordan: Hungry Man
Louis Jordan/Ella Fitzgerald: Patootie Pie