you can't buy latam flights on ba with cash if that's what you mean - ba have no interest in selling them unless connecting to or from a ba flight. so buying an economy ticket with cash and trying to upgrade with avios won't work.

with reward seats you have to just take what is available as i suspect other have already booked any business reward seats on your outbound date. you can book economy, and if business availability appears in the future you can change the booking to take the business reward seat. you can try it online in manage my booking, but i suspect you may have to call. the cost would be any difference in avios and taxes/fees/charges, and a £35 per person change fee.