Some possibilities:
AA or UA - ORD / SFO then a commuter to FAT
AA or UA - ORD / LAX then a commuter to FAT
UA ORD / LAS then a commuter into FAT
DL ORD / SLC then a commuter into FAT
US ORD / PHX then a commuter into FAT
My choice:
AA ORD-DFW-FAT (farther, but all mainline and more miles (this is FlyerTalk, after all

)