Frank Larking Genealogy Search

In 2011 my father started a search for his great-grandfather’s lineage. My father died in 2013 and wasn’t able to complete his search so I am here now picking up where he left off.

According to my great-grandmother, Leila Larkin(s), her father was Native American and she thought he was Cherokee, possibly only partially. There is some discrepancies in surnames on numerous documents I do have. The surname is some form of Larkin/Larkins/Larking/Larkings. Here is what I do know:

Walter Frank Larking (sometimes Larkins) was married to Cora Spradling on February 14, 1920 in Auburn, Nebraska. Their children were Don, Johnathon, Leila, Irene, William, and Wayne. Walter was born in Texas either in 1895 or 1896 and possibly in Fort Worth. On his marriage license it lists his father as Frank Larking and his mother as Nellie Brown (though on some documents she is listed as Edna Mae Brown).

I am looking for any information in regards to Frank Larking (possibly Larkings) and his possible Native ancestry.