Military records from World War I - present are held in the National Military Personnel Records Center (NPRC), in St. Louis, Missouri. See http://www.archives.gov/research/order/vets-records.html#nprchttp://www.archives.gov/research/order/vets-records.html#nprc for a list of holdings and ordering information.
There is no guarantee that any record found would have family information.
There are World War I Draft Registration Cards also available at Ancestry.com (requires subscription) and the National Archives at https://eservices.archives.gov/orderonline/start.swe?SWECmd=GotoView&SWEScreen=GPEA+Catalog+Screen+FFO&SWEView=GPEA+Made-To-Order+Reproduction+Landing+Page+View+FFO. These were for males born between 1873 and 1900. There were three different registrations: 5 June 1917 for men aged twenty-one to thirty-one; 5 June 1918 for men who had become twenty-one since the previous registration; and 12 September 1918 for men aged eighteen to twenty-one and thirty-one to forty-five. The last group would include the person referred to, but the registration card contains no genealogical information other than age, address, occupation, and whether a native American on non-citizen. I'm not even sure that Ancestry.com has the 12 September 1918 cards.
If the person of interest was already in the military in 1917 - 1918 he would not have been required to register for the draft. His death certificate should indicate place of burial. If so, you might check the grave for a military style marker or a marker with the date of death and look for an obituary from a local paper.
You might post to one of the military service forums. There are several and you can find them by clicking on the "General Topics" link at the upper left of this page then scroll down to the Military Service section.