It would have been a fantastic save if he'd kept it out and he nearly did.
I've just watched that second goal again very carefully and when the throw is taken, Silva is standing just off King and Kolarov is marking Slimani. The ball comes in and Fernando challenges the Leicester player , who just wins out. Silva has moved towards the ball and left King free while Slimani moves back a couple of yards, Kolarov doesn't go with him and no one else picks him up. So he picks up the second ball and knocks it back to King, who hasn't moved from where he was when the throw is taken. If Silva had stayed where he was at that time and just kept an eye on King, he'd struggle to get that shot away or it would be blocked by Silva.
And the goal Burnley scored was another where we failed to pick up an opposition player just outside the box at a set piece and he's got to the second ball virtually unchallenged. It's something we're very poor at generally.