OK. I can answer my own question here in case it's of any use to anyone else.
If you have a simple one way or return, using the Amadeus PNR you get from a BA Avios booking seems to work.
Once it has accepted the BA PNR, you actually see the SABRE PNR in your Latam App on the phone, not the BA one.
For anything more complicated you need the SABRE PNR.
All I had to do was ring up the executive club and ask for the 'alternate airline locator' for the booking.
That plugs in to the Latam website just fine.
But I don't think there is any way to find this alternate PNR even looking through Finnair or Royal Jordanian, you have to ring.