Carolyn --
Was there a middle initial for this man? As you mentioned, William Fleming served in Co. "B", Terry's 8th Texas Cavalry, later led by Col. Harrison.
However, given what the obituary states about service in Mississippi, there are other possibilities. For instance, William J. Fleming, Co. "C", 2nd Texas Regiment, and Co. "F", Waul's Texas Legion. Not sure about possibilities for Fleming at Yellow Bayou or Pleasant Hill, both in Louisiana.
We'd have to look at the service files to see if this man served in several diffeent Texas units, or just one.