DonaldT -
I was intrigued by your inquiry and the fact that Feel Lucky was bred in Texas. He was bred in Texas before pari-mutuel wagering had (most recently) been made legal by the Texas Legislature after a long interval of its being illegal - which gave impetus for the three existing Tier One tracks in operation today and to my knowledge there was no 'Texas Accredited Bred' program or breeding incentives program for thoroughbreds in Texas at the time. Still, that lack of a state based breeding program's infrastructure did not keep Texans from breeding and racing thoroughbreds, many of some note, but it was somewhat unusual to do so from a base in Texas. I am probably repeating research you've already done but followed the "Breeder" and "Owner" information on this site of his female family backwards through to Miss Dundee, Feel Lucky's 4th dam, where the continuity of his "Cowan" breeding connections began. (B/T/W - his 5th dam, Despondent '36, was a Whitney bred mare, subsequently owned by Ogden Phipps. Miss Dundee and her subsequent offspring were Kentucky bred, owned and apparently raced by the Cowans until Treat Yer Teacher, who is listed as Texas bred by Claude Cowan, the dam of Kindergarten Kid, dam of Feel Lucky (and others).
Then I searched for Claude Cowan and quickly found this article at the following link. It doesn't mention Feel Lucky but gives a good idea of Feel Lucky's "Cowan" breeding connections and their connection with Texas.
http://www.bloodhorse.com/horse-racing/articles/9116/breederowner-claude-cowan-jr-dead-at-77Treat Yer Teacher was a "Cowan' Kentucky bred mare who was apparently moved to Texas as a broodmare, and bred to Rhymeroni a Texas bred stallion who had also been raced by Claude Cowan Jr., he being sired by the Texas based Dancing Dervish (a son of Native Dancer) - Both Rhymeroni and his sire, Dancing Dervish stood stud at the McGregor Ranch, Witchita Falls, Texas and apparently stood to both thoroughbred and quarter horses mares.
With this continuity of breeding and racing connections anchored to the Texas Hereford cattle raising industry and towns such as Wichita Falls, Archer City and Dundee for whom the 'blue hen' mare that gave rise to this Kentucky and eventually Texas based legacy of racing thoroughbreds, etc. I would think you might find a winner's photo among the archives of those towns local papers, if the tracks where the stakes races were held do not have them. You might also check with the Library and historical sources available in Kentucky - their staff are very helpful and quite a lot of their resources are available online.
Good luck - I enjoyed tiptoeing back thru the steps of some early Texas bred thoroughbred history !