BA really isn't any help. You're lucky if they give you the right contact info for bagport. Same exact thing happened to me.
Bagport is one of the most ridiculous orginizations I've ever dealt with.
If you call and they feel like answering the phone (unlikely), they probably have used all their motivation to pick up the phone, so don't expect them to actually be helpful. If you e-mail, don't expect a reply any sooner than 2 weeks.
And then, finally, If they do recover your item, they will extort 15 quid as an "administrative fee" plus inflated shipping fees that in total, are just a little cheaper than your kindle.
I obviously didn't expect them to jump through hoops. Ideally, BA might have looked at who was sitting in that seat and discovered I had a 5 hour layover in LHR and could have easily dropped it off at the GA only a few gates down. It would have even been OK if BagPort was responsive and provided good service. I'd have no problem paying them for good service. But you will not get that.