So going by the boarding passes on Sam's fridge the flew the following airlines. I think the flight numbers are correct - the Instagram pics are a tad blurred. I notice that Flight Centre got frequent mentions during the broadcast so they obviously bankrolled some of the trip.
Fri 11 Sep MEL/DXB QF 009
Mon 14 Sep DXB/LHR QF 009
Tue 15 Sep LHR/JFK BA 117
Tue 15 Sep JFK/BUF B62002
Thu 17 Sep YYZ/CUN AC1810
Fri 18 Sep CUN/DFW AA1655
Fri 18 Sep DFW/SYD QF 008
I notice that from the website
The BA Source | that the rego of the 744 that operated BA117 was G-CIVF so they obviously used file footage of what was meant to be their plane landing in New York as the rego on the nosewheel flap on the show IIRC was "LS" which would have been G-BNLS. This aircraft had it's last hurrah when it flew from Cardiff to Victorville as BA9156 on 20 May 2014 so definitely not that a/c but I don't expect the majority of Sunrise viewers would have been as picky as die hard avgeeks here on AFF.
I note that 744 G-BNLH has also been withdrawn from use. It was appropriately nicknamed "never leaves hangar" for obvious reasons. Any plane that got parts from that a/c would be jinxed for sure.