I did call BA and they told me there is no IT glitch which is what I thought may have Brent he case prompting me to call them.

They suggested I call LAN which I did. LAN advised me that there are plenty of seats available and that I should call BA if I wanted to book using avios.

I called BA again who said they can't see anything on their system and to try other partners.

I called American Airlines just now and they have some availability.

Why would BA show no availability for seats they had plenty of availability for and another one world partner has confirmed availability of some of the seats?