Kangaroos is a 9 letter and therefore invalid word.
Unfortunately, 'Katzenjammers' is NOT a valid word on dictionary.com (katzenjammer
is, but there is no sign of 'katzenjammers' on dictionary.com so as per the rules I can't allow it, sorry.)
klinefelter is an 11 letter and therefore invalid word.
Kindergarten is a 12 letter and therefore invalid word.
Kindergartner is a 13 letter word AND is valid on dictionary.com so therefore, Jayson scores a point and wins immunity for Genovesa.
I will give this final decision to Chris as it is his game when he gets on if y'all wanna challenge it, but as per the rules stated earlier, that is my result.