Dear Ms. Rozycki,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the series Applications for Enrollment in the Five Civilized Tribes, 1898 - 1914 in the Records of the Bureau of Indian Affairs (Record Group 75) that contains a file card for Hiram King. It has been digitized and available via the Catalog. We also located 7 file units in Record Group 75 that relate to the roll number of William King that have been digitized and available via the Catalog.
We hope this is helpful. Best of luck with your research!
[Information provided by Cody White, Subject Matter Expert]