There are 318 seven-letter words that start with K in the ENABLE word list used by this site. That is about 1.4% of all seven-letter words. The highest-scoring is kolkhoz, worth 27 points in standard Scrabble tile values.
Different games use different word lists. Check unusual words against the list your game uses.
Highest-scoring seven-letter words starting with K
kolkhoz27 points
kolkozy27 points
kolhozy26 points
kibbitz24 points
kibbutz24 points
khazens23 points
kickoff23 points
kwanzas23 points
kyanize23 points
klezmer22 points
kumquat22 points
kvetchy22 points
kebbock21 points
kebbuck21 points
khirkah21 points
killjoy21 points
kajeput20 points
keyways20 points
klutzes20 points
knuckly20 points
kolacky20 points
kreuzer20 points
kunzite20 points
kayaked19 points
Patterns in this list
The most common second letters are ki (93), ke (70), ka (51), kn (39), ko (23). 124 of these words contain three or more vowels, which can make them easier to spot when you are unscrambling.