Dear Ms. Colbert,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located a series titled Settled Case Files for Claims Approved by the Southern Claims Commission, 1871 - 1880 in the Records of the Accounting Officers of the Department of the Treasury (Record Group 217) that included 7 file units for Natchitoches, Louisiana but do not include one for Emilie Kirkland. Please check with the National Archives at Washington, DC - Textual Reference (RDT1) as to the availability of a file for Emilie. RDT1 email address is firstname.lastname@example.org.
We also searched Fold3 and located a file for Emily/Emilie Kirkland. Since there may be a fee for using Fold3, you may view these records online at one NARA's facilities for free via a NARA PC. For the nearest NARA location, please consult the web page at https://www.archives.gov/locations/.
We hope this is helpful. Best of luck with your research!