There are 121 4-letter words starting with K in the ENABLE dictionary — 3% of all 3,903 words at this length. At 5 points, K is worth more than most tiles without being awkward enough to hold back for — it is generally better placed than saved.
The list divides into 11 groups by second letter, the largest being the 29 words with ki. Scanning the right group is faster than reading the whole list, which is why it is broken up below rather than run alphabetically.
If you know more than one letter, this page stops being the fast way to find it. Enter what you have in the unscrambler — the Contains, Starts with and Ends with filters combine, and setting both length fields to 4 narrows this list to the handful your letters actually allow.
All 121 words, by second letter
KA… (26)
kaas kabs kadi kaes kafs kagu kaif kail kain kaka kaki kale kame kami kana kane kaon kapa kaph karn kart kata kats kava kayo kays