maybe if you wet it and let it dry flat it could work

What Tomas said. 

If you use alcohol, it will dry faster but you may have to do it two or three times.

Very, very, very low heat while drying will also help but that will depend on how the leather was tanned, vegetable tanned has a tendency to get hard as a board.

And you may want to try saddle soaping it and then drying it under a flat weight.  Or using one of the non petrol based waterproofing agents such as Mink Oil.  Some of those will darken the leather. 

Option of last resort is Neatsfoot oil.

Ultimate last resort is Vasiline but it leaves the leather tacky and greasy feeling.

steam iron on  a low heat setting

stick it under your saddle and ride the range !