In the American CW Database I found four William H. Fleming's, one being only 17 and I found 22 William's, no middle names.

Of the three W. H.'s, there is no mention of wounds or deaths.

George Martin

William H. Fleming

Residence was not listed;
Enlisted as a Captain (date unknown).

Intra Regimental Company Transfers:
* from company B to company D

"B" Co. TN 25th Infantry

William H. Fleming

Residence was not listed;
Enlisted as a 1st Sergeant (date unknown).

"E" Co. MS 20th Infantry

W H. Fleming

Residence was not listed;
Enlisted as a Private (date unknown).

CS Gen & Staff