The information in our Native Plant Database on the species page for Rhus lanceolata (Prairie flameleaf sumac) says that it is unisexual and monoecious. Unisexual means that it has flowers that are strictly female with pistils containing eggs that can grow into seeds if fertilized and it also has separate male flowers with stamens that produce the pollen. (The alternative, bisexual or perfect flowers, have both the pistils and stamens within the same flower.) Monoecious means that the two types of flowers, male or female, occur on the same plant. (The alternative, dioecious, means that the male flowers occur on one plant and the female flowers occur on a separate plant.) You can see a line drawing of the two types of flowers on p. 235 of Shinners & Mahler's Illustrated Flora of North Central Texas.
Robert Vines in Trees of Central Texas (p. 249-252) says that Rhus copellina has flowers that are "polygamo-dioecious". (Rhus copellina var. lanceolata is a synonym for Rhus lanceolata.) Vines definition for polygamo-dioecious is:
"Essentially dioecious, but with some flowers of other sex or perfect flowers on the same individual."
So, what all this is attempting to say is that I don't really know for sure why your flameleaf sumacs don't produce more seed. It is possible that your plant doesn't produce many female flowers (and/or perfect flowers if Vines' description of the breeding system is correct) that can make the fruits.
There are other possibilities as well. It could also be that:
Without seeing your trees, it is impossible to say for sure what the reason is for the lack of fruit.