Road Trip - Chicago to Flint, TX (Texas BBQ suggestions)
Purple Pig Cafe is in Flint (and Canton), Texas, but the specialty is a pulled pork sandwich with coleslaw atop it akin to what you would find in other parts of the South ... http://www.purplepigcafe.com/about-us...
P.S. The epicenter of Texas BBQ [beef[ is in what is called the Hill Country, which is in and around Austin, Texas [for a generic definition of the area].
We have a couple of ETx posters who check in from time to time but it's not my part of the state so I can't help much. Only place I've heard much about in the general area is Clark's in Tioga. You may pass close by on your way thru. You're very close to Tyler; here's a thread about Tyler bbq with some suggestions:
The poster Mike C. Miller seems to be very knowledgeable. I'd use the search feature for other towns in the area and watch for his recommendations.
BTW if you're looking for bbq on a Sunday, many places will be closed.