Can you please tell me the month/year the 1885 Omaha City Directory was published?
Unfortunately the title page just says 1885. No month is given. The directory was compiled and published by J.M. Wolfe. I did find Mr. Thomas listed with his company in Saratoga Precinct, Omaha (that would have been Fort Omaha) in the Nebraska 1885 state census, which you can see free on FamilySearch. That info would have been current as of June 1, 1885. Unfortunately the census taker did not bother to fill in personal details for any of the soldiers, but it does give their company: Company E, 4th Infantry, of the U.S. Army. You can also find him listed in the U.S., Returns from Military Posts, 1806-1916 database that is available in the Ancestry Library Edition (also the personal subscription version, if you have that). I am emailing you a link where you can download that image--he is at the bottom of the page. We also have these records on microfilm at the W. Dale Clark Library, as well as some information about Fort Omaha.
I hope this helps! Let us know if you have any further questions.