Subject to the inevitable seniority, and it is a pretty senior aeroplane (in all seats), any BA pilot with a reasonable amount of experience can fly it. I think there used to be a requirement for an interview with the fleet management - not sure if that still applies.
The only down side is that as a FO, you're tied to the type for seven years so it doesn't allow a lot of flexibility career wise. Still, would be nice to have a go ...