Why is the King of Spades the best opening lead with this hand?
Against No Trump the point is to set up tricks that will be guaranteed.  Here the KQJT9 is four safe tricks - so you lead from that hoping to later get in with the diamond King.
When you do get in, either with a spade from partner or a diamond, you have four tricks guaranteed that will set the contract.
By convention, from a run like that you lead the top one (to let Partner know you have the next one or next several).
Beyond that, Kx is a bad lead because it doesn’t set up a trick and if the ace is to your right it gives away a trick. Since right hand opponent has bid 1NT, they probably have around 16 points (A=4 K=3 Q=2 J=1) out of 40 total, while left hand opponent has between 9 and 12 or so points. So odds are RHO has the ace, and so your diamond K will be a trick if you don’t lead from it.
Most of the time in bridge in no trump you either lead a high card when it’s next to another high card or two (so leading it and knocking out the one above it makes the one below it a winner) or you lead a low card in a suit you have a lot of cards in. (In a trump contract you might lead a suit you’re short in, also.) That’s of course when you don’t know what partner has (as is true here).  A low card from length (usually your 4th highest, or near that, depending on your agreements) tells your partner what to try and lead back - even a 65432 suit can become a trick or two in no trump if nobody else has more than three of them!