He married Isabella Rachel Kimbro (Titus), daughter to James Titus, a VERY PROMINENT man, and personal freind of Sam Houston, AND a Texas State Senator. He was VERY wealthy as well. In an 1860 census, WH Fleming had a net value of $30,000 (about $9 million in todays wages). He was in his 50's when the war started. I have found notes of service in the Mexican American War, and numerous militia call ups for a William H. Fleming prior to 1855. This would correspond with the "round-bout" time James Titus passed away, and would have left his daughter a sizeable chunk of land and property, and WH Fleming being the Oldest Surviving Son would have moved to an Estate Management role.
On an interesting note, WH Fleming's daughter, Polly McCraw Fleming marred Granville Everett Peek, who was a Sargeant in the 9th Texas Cavalry...
Hope this helps. I have a pretty extensive paper on the Flemings, and would be glad to share it with anyone who wants it.
thanks,
PH