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Found the following possible matches.
World War 1 registration card
Possible Match found on find a grave
His wife remarried.
Family tree on familysearch.org..family search is a free website. You just need to register to search
Dear Ms. Krom,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the series Returns of Military Organizations, ca. 1800 - 12/1916 in the Records of the Adjutant General's Office, 1762 - 1917 (Record Group 94) that included the digitized returns for the Eighth Infantry: 1906-1910 and Birdie W. Thomas (see Images 245 & 348). The images are available using the Catalog. Since he was dishonorably discharged, we located the Court Martial Case Files, 1800 - 1917 in the Records of the Office of the Judge Advocate General (Army) (Record Group 153) that may include a file pertaining to Birdie W. Thomas. For access to the non-digitized case files, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at email@example.com.
We also located the Orders and General Correspondence, 1/1872 - 6/14/1934 of Alcatraz Island in the Records of U.S. Army Continental Commands ( Record Group 394) that may include General Order No. 71 dated 22 April 1909 pertaining to Birdie Thomas. For access to these records, please contact the National Archives at College Park - Textual Reference (RDT2) at firstname.lastname@example.org.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT1 and RDT2. We apologize for this inconvenience and appreciate your understanding and patience.
We hope this is helpful. Best of luck with your research!