The only Glendavagh in Co Tyrone isn?t near Castlederg. It?s in the south of the county, near Aughnacloy. There is an Alexander Kyle recorded there in Griffiths Valuation for 1860 which lists him on plot 21a (house, an outbuilding an 1.5 acres of land). That?s near the modern Glendavagh Rd, just south of Aughnacloy.
Possible death for Alexander registered Dungannon Apr ? Jun 1886 Volume 1, page 416. Gives an estimated year of birth of 1816. He doesn?t appear to haveleft a will.
Some family still in Glendavagh in 1886, who were Church of Ireland.
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Ballymagran/Glendavagh/1733839/
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Ballymagran/Glendavagh/1733836/
Glendavagh is in Aghaloo parish. The Church of Ireland records for that parish start in 1791 (with gaps). A copy is held in PRONI, Belfast. You may be able to find Alexander?s birth, and perhaps his marriage there (assuming his wife attended the same church).