Any seed mix is going to need water to get it started. The ladino, trefoil, and alfalfa are all perennial and should come back each year. Ladino will grow well in TX if it gets enough water, it can survive drought well but will not produce forage well in drought conditions. The trefoil can be slow to establish and should be allowed to make seed at least once per year to keep it ging well. Trefoils are also more adapted to areas north of where you are at. Alfalfa can be tough to establish on some soils and most varieties are adapted to areas more northernly than TX. The buckwheat and flax will not come back as they are annuals. The cowpeas also will not come back and do not do well on all soils. Other then the flax this blend is basically a deer food plot mix. The cowpeas also will not live well into the winter (even in TX) as they do not tolerate cooler temps. The flax may not live either. Best to wait until spring to plant.
I know this blend is supposed to raise Omega-3 levels in eggs, but there is plenty of evidence that shows just having pasture available will raise the Omega-3 levels significantly. At $150/ 50lbs this is a very expensive seed blend - right up there with the best alfalfas and annual ryegrasses.
For the Austin area I would recommend these forages:
Annual Ryegrass - does well in south, Gulf coast, reseeds well
Alfalfa - only varieties adapted to the deep south
Arrowleaf Clover
Crimson Clover
Subterranean Clover
White Clover (smaller leaved Ladinos or Dutch white probably better for chickens)
Bahiagrass - warm season
Crabgrass - yes, it is best known for being a weed, but it is also a great pasture forage, highly nutritious
Those would be a few that should grow well there. Some are more toleant of drought than others. Some of these in a mixture will cost more than the "chicken forage" but you can be sure that the plants will grow where you are at. That is the problem with mixes. Unless they are created for a specific location they are made with a little of this and that so that something will grow when you plant it. Rarely do all of the seed live up to their full potential. Also remember that not all forages will grow in all soil conditions. A soil test can save a lot of frustration and wasted money.