Braniff built up quite a number of 707 variants between 1959 and 1969, and then disposed of them all in the years following. Surprisingly the 707-327Cs were the first to go.
They got 9 of them in 1966-67, which were linked to the Vietnam contract, but lost this at the end of 1970. All but one were then sold by mid 1971, the survivor, N7104, lasting until 1973, I am guessing for the Hawaii flight.
It was only after all these modern 4 or 5 year old aircraft were disposed that Braniff then started selling their four custom 707-227s, followed by the five 720s. The secondhand 707-138Bs stayed on line until 1973, when they went, along with that last -327C.
The DC8 (including some secondhand ones) took over South America completely, plus a few domestic sectors, but the bulk of the 707s were replaced by 727s.