When you say "bookings" do you mean three tickets? If so, BA will not interline. Yes, BA has an interline agreement, but as with many carriers, will only perform the service if you are on a single ticket.

This does not prevent the possibility that any given agent on any given day might do this for you. But, as it stands, you should plan on retrieving your bags at AMS and HKG and then checking back in for your onward flights.