I've been using kosher salt for all my kimchi and never had any problems. You want to avoid some sea salt and all iodized salt.
My recipe for Mak Kimchi
5 pounds Napa Cabbage
1 and 1/4 cups coarse sea salt or Kosher salt
Kimchi Stuffing
2 tbsp sweet rice flour or all purpose wheat flour
2 tbst finely chopped Saeu Chot (salted shrimp)
1 cup Gochu Garu (Gochu pepper flakes)
1 pound Korean radish or Daikon, cut into 3 inch matchsticks
1 red Gochu pepper, seeded, deribbed and cut into 1/4 inch strips
1 green gochu pepper, seeded, deribbed and cut into 1/4 inch strips
4 scallions, white and pale green part only, cut diagonally into 1/2 inch pieces
2 scallions, white and pale green part only, cut into 1 and 1/2 inch pieces
2 cloves garlic, peeled, crushed and finely minced
1 tbsp freshly grated ginger root.
1/2 cup sugar
1 tbsp lemon juice
1/2 cup chopped, freshly shucked oysters
wash cabbage and remove tough outer leaves for later use. Coarsely chop remaining cabbage and spread out in a large non-reactive bowl (stainless steel is fine). sprinkle with a cup of the salt and stir to mix. add remaining salt to a cup of lukewarm water, stir to mix and sprinkle evenly over the cabbage. Let sit for three hours, stirring every half hour to evenly salt the cabbage. The process will pull a lot of water out of the cabbage, but in the end it should still be crisp, like a dill pickle. Discard salt water and rinse the cabbage several times in fresh water and squeeze out between rinses. Set aside in a colander to drain and make the stuffing.
Dissolve the rice or wheat flour in a cup of water and bring just to a boil. Reduce heat to low and simmer for two minutes, stirring constantly until it becomes a paste. Let cool. In a large bowl, combine flour paste, salted shrimp and pepper flakes, mixing well into a bright, deep red paste. Stir in cabbage and remaining ingredients. Pack into sterilized jars. Wipe up any remaining stuffing with the outer leaves reserved earlier and press the leaves down in top of each jar. Add enough sterile water to cover, but leave at least two inches of space at the top of the jar for expansion. Let sit at room temperature overnight. Taste brine for saltiness and add salt or sugar to adjust to your preference. Let mature for 2 or 3 more days at room temperature and transfer to refrigerator to stop fermentation. For more tang, leave out at room temperature for 1 more day. The kimchi will stay fresh for a month in the refrigerator, but will gradually become more sour.