Ask Mr. Smarty Plants

Our Native Plant Database does not have a sumac with the common name "flaming sumac" so we are betting that Rhus lanceolata (prairie sumac) which also has the common name "flameleaf sumac" was sold to you with the trade name 'Flaming Sumac.'  Sumacs are difficult to transplant because they are a suckering plant and making sure you get some roots along with the sucker is sometimes a problem. 

In terms of what is causing the decline of your trees, the first thing that comes to mind is transplant shock. You transplanted them at the right time, and they leafed out in the Spring, but sometimes transplant shock can show up as much as 3 years later. If you purchased the plant in a pot from a nursery, it may not have been properly placed in the pot, with damage to the roots, or even have been in the pot too long and become rootbound, which would mean as the tree developed in the Spring, it needed to put roots out into the native soil around it, but the roots were running round and round in the root ball and could not break out. In our research, we learned that too much irrigation or fertilization can lead to plant decline. As with most native plants, the members of the Rhus genus do not need fertilization. The sumac does, however, need some deep watering the first year it is in place, if there are not regular rains.

On the subject of disease, we found one reference to fusarium wilt in sumacs, but when we researched fusarium wilt, we discovered that it is mostly tomatoes that are affected by this, and that cotton root rot is also a fusarium wilt. But we also found a reference to verticillium wilt in sumacs, and then found several research articles on that. It sounds much more plausible that this is the problem, considering the description of symptoms that you cited.  From the USDA Forest Service on Rhus Copallina (closely related) we extracted this rather depressing quotation:

"Verticillium wilt causes wilting of individual stems, followed by death of the foliage. Eventually the entire plant dies. Prune out infected branches. Do not replant in the same spot with sumac or other susceptible plants."

Verticillium wilt is a soil-borne disease, and treatments for it are few and chancy. Usually the recommendation is to get those plants out and destroy them, and then be careful not to plant another woody plant which can also be susceptible in the same area, Here are two websites with lists of susceptible and not-so-susceptible woody plants when you are considering replacement:

Trees for You, Verticillium Wilt, a Disease that Attacks Trees from Inside Out

University of Minnesota Extension Verticillium Wilt of Trees and Shrubs

From Google, here are pictures of Verticillium Wilt in Sumac.

We are sorry we couldn't give you better news. We are not plant pathologists and can only guess, based on our research, what the real problem is. For some more information, we would suggest you contact the Texas A&M AgriLIFE Extension Office for Hays County.