I have another Ambrose McKee at Rutherford Co TN in the early 1800 time frame and I have speculated that he is a brother of your Jane (Jincy) McKee Elrod.
My Ambrose' father was John McKee of Mecklenburg Co NC.This John is brother to the Ambrose Sr.
The person who may have found the best evidence about Jincy that I know of doesn't seem to be online for genealogy now, her email name was mizzykaz.Her ancestor is the James McKee, also at RU Co TN, who married Polly Sullivan, these also being of Mecklinburg Co NC.I haven't worked on the Rutherford aspect for some time.
My Ambrose was born about 1800 in NC per census.He married Martha (LNU) of VA who was born 1801 per census.He left Rutherford Co TN after the 1830 census but before 1833 when he has a daughter born in Franklin Co AL.He is in Franklin Co AL for the 1840 census but moves to Hardeman Co TN before 1847.
I wish I had more info to share with you.Good luck.Linda McKee