Fold the turn. You are NOT going to beat 6 players with 4 to a straight with KK on this board, not to mention the FD.

River fold is good, some math:

There is a chance no one is on a FD, but even then if we split the pot 5 ways playing the board you need a 1/5 chance that no one holds a 9.

Even making the reasonable assumption that at least two 7's are lie in other peoples hole cards this leaves 6 unaccounted for hole cards; about half the time there will be a 9 in someone elses hand (54% assuming a random distro). This is a clear fold.