The question is quite simple, does Jaime Lannister have any claim to the Iron Throne? In other words, how far down in the succession is he?
After all, his sister is currently the Queen, so if she dies does he get the Throne? The succession is not quite clear, but Jaime is related to the current Queen and has the support of the Lannister armies (not so clear after the last episode though I have to admit).
A similar question asks about why Jaime didn't the Throne after killing the Mad King which is a very different situation, so mine's not a dupe.