The way I see this situation:
Kobe is 1v1 in transition vs Alec, dribbles the the ball on the right block slightly above the baseline, which is good since it prevents someone from spotting up in that corner or cutting baseline.
Alec gives up a lot of space potentially because he was the only defender when Kobe established the deep post position, in order to not give him a chance to spin around him for an easy layup.
You see Withey busy focusing on the ball and Kelly simultaneously. Randle was the one trailing the play, never arriving until the shooting motion was already ongoing. Booker was switched onto Clarkson and Millsap waited on top of the key for Randle to trail the play, while Booker after short hesitation in the paint where he probably considered double teaming Kobe communicated with Millsap he'll switch onto Clarkson for the possession and afterwards he went to Clarkson who moved towards the weak side corner slowly when Kobe initated his final move.
I suppose the idea of the defense in this situation is that Withey at first stays in the paint to help if Kobe goes towards the middle while staying within reach of Kelly and Burks job is to take away the baseline primarily.
Kobe chose probably the most difficult of all shooting options in that situation, and Burks contested. You can't close out to a fadeaway shot too hard since you can't limit his landing spot and risk a foul if you do in that situation.
I think the proximity of the shot was mostly caused by this being an early offense/transition possession which allowed Kobe to get this close in the first place without much effort.
Another strategy could have been a soft double by Booker to force the ball out of Kobe's hands before Randle arrives by using the extra body. But that would have required Millsap to not wait around the nail, but switch back onto Clarkson.
Had Withey doubled he'd have risked an easy pass to Kelly and I guess it's more the Jazz defense style to have the help defense rotate over late since the majority of the minutes you have to replace Withey with Gobert who is the stifle tower
tl;dr: The vine doesn't show it's a contained fast break attempt by Kobe and communication probably caused the defense not to double.
Burks played smart and within his limits.