You have to play the best 5 cards you can.

Kid one's hand is

Kid two's hand is

So Kid one has a higher (better) flush, and he wins

The term kicker is misleading in this case. The cards they hold are both used in making the hand. In another situation:

Player 1 has
Player 2 has

Board is

Player one's hand is
Player two's hand is

Player two would win because he has the best hand either of them can make.

If we change the board by one card though...


Now...
player one's hand is
player two's hand is

They both hold hands of the same value and they will split the pot.