I got the year confused (due to the two Dallas Texan teams).
The 1960 era Dallas Texans, which moved to KC, were an AFL team.
The NFL Dallas Texans lasted one year -- 1952 -- and are considered the last NFL franchise to fail. They pretty much took over the failed NY Yanks players, but weren't considered a continuation of that lineage. The Baltimore Colts started in 1953 and took on many of the Texan players, but are considered an expansion team and new franchise.
So the Dallas Texans are considered a one year franchise which failed.
Apparently had a rough season and the last few home games were played in Hershey PA and one in Ohio.