Click for a list of Lodges in Ontario
It appears to be a Canadian organization, active in the 1860s and 1870s. It was certainly active in Nova Scotia in 1867 when a degree book was published in Halifax1, and in Ontario in 1868 when both the Most Worthy Grand Lodge and the Worthy Grand Lodge of Ontario were listed in the Toronto city directory. It is not listed in Stevens.
At some point the Order of British Templars and the British-American Order of Templars united, seemingly in Cobourg, Ontario2.
There was a county lodge for Yourk County in Toronto in 1868.
References:
(1) https://archive.org/details/cihm_16175
(2)http://books.google.ca/books?id=q2wZAQAAIAAJ&pg=PA419&lpg=PA419&dq=%22British+American+Order+of++Templars%22&source=bl&ots=Ku2nqbCzff&sig=Gj1G5DWrBodjsV9MGiaciJ1PypU&hl=en&sa=X&ei=88O2U_DbJ8Hd8AGwyoHQAQ&ved=0CBwQ6AEwAA#v=onepage&q=%22British%20American%20Order%20of%20%20Templars%22&f=false