When people use the phrase "prog" they aren't using it as short for the word "progressive", they are using it to describe a style of music. "Prog" is marked by heavily orchestrated, composed, and arranged music, with little (if any) room for improv.
Jazz is all about improv.
I have no doubt that JR could play jazz, and he is an improv-ing beast, but other than a few brief moments here and there, I don't see any jazz influence whatsoever in DT's discography.