I am inclined towards the St Celsus Old Churchyard
http://bit.ly/1wZdD5d . I would suggest you establish contact with Fr. Vincent Sherlock,
http://sherlockshome.ie/contact/. I have his email address but feel it inappropriate to pass on without his consent.
The Church of the Immaculate Conception is the principle church in the parish and the others act as satellites, and I feel any documentation will always have the principle church given as the place of baptism or marriage even if the event was in one of the smaller churches.
Tavraun like Sinolaun/Sonvolaun is west of the site Cloonamna School which on balance points to the Kilkelly area. My folks were east of the school and the next house on the road was in Sinolaun and only a few yards west of the school. They both drew water from the same well but attended different churches in the same parish.
I have seen a list of headstones at the more recent Culmore cemetery (in use) and your Flatley family are not given, and may only be a partial list. The Naomh Mobhi cemetery dates from the mid 1940’s as I believe the Culmore (in use) cemetery also does. This only leaves St Celsus in Kilkelly and a remote chance of it being St Brigid's Cemetery. Urlaur Abbey, given that the Thomas you refer to died pre 1900.
I wouldn't be too distracted by the 1851 census Flatley was a common name in the Parish and he with the dancing feet fame, from Lord of the Dance and Riverdance can claim a common heritage to a Flatley family from Kilmovee also.