You didn't mention his state of residence, which people will assume to be Tennessee. I'm guessing that you're asking about William D. Pounds of Milltown, Chambers County AL. A regimental historian gave his date of death as June 27, 1862; the service file for Wiliam D. Pounds states his date of death as June 30, 1862. Since casualties were higher at Frayser's Farm, I'm guessing the latter date to be correct.

A number of family researchers give the place of death as Chattanooga, Hamilton County TN. This is certainly wrong.
Casualties were reported in local newspapers soon after the fighting ended. In the summer of 1860, a newspaper editor reported eighty-two newspapers, daily or weekly, being published in the State of Alabama. Since Chambers could be found on the border of Georgia, casualty lists could have been published in that state as well.

Here's a sample from the Richmond Daily Dispatch of June 28, 1862 --
http://imls.richmond.edu/cgi/t/text/text-idx?c=ddr;cc=ddr;idno=ddr0513.0022.154;view=text;rgn=div3;node=ddr0513.0022.154%3A9.1.2
Here's another for the daily edition of June 30th --
http://imls.richmond.edu/cgi/t/text/text-idx?c=ddr;cc=ddr;view=text;idno=ddr0514.0022.155;rgn=div2;node=ddr0514.0022.155%3A6.1
You'll need to copy and paste the entire URL on your address line in order to read.