What is Ron, deltaRon, and Ron flat for an TS12A12511 ANALOG SWITCH?

Nat,

Take a look at this application note "Understanding and interpreting standard logic datasheets" page 39

Ron and deltRon

Ron flat

On-state resistance for a signal switch will vary based on the input/output voltage on the drain or source changing the FET Vgs.  Ron flat is the difference between the lowest and highest Ron value or how flat the ron vs input/output voltage curve is.