King's Rock is best used with Pokemon that have the Skill Link ability and can use a variety of multi-hit moves. Cloyster is a notable example, as it can use Shell Smash and either Icicle Spear or Rock Blast to tear through the opponent's team. Assuming the attack hits, Cloyster will have a 41% chance of flinching the foe. Another example is Cinccino, which can use King's Rock along with moves such as Tail Slap or Bullet Seed. Aside from these Pokemon, King's Rock is generally a bad item to use in competitive battles.
Yes, each hit of a multi-hit move will have independent chance of causing flinch. In the case of a Pokemon with Skill Link, the total chance of flinching is 41%.
Smogon - King's Rock