I have found myself badly wanting to write a thing, and feeling like it has to sit so long in my head before I can get it out. And sometimes it does have to sit first; but I wonder if I were more willing to say the wrong thing in the wrong way, if I could get at the right way sooner.
How much harder is it for our kids, who may not have any idea what they want to say to start with? It comes down to free writing. Not only is it free of rules, but it's truly freeing. It frees the ideas that are locked in the minds of our kids, it frees them of fears, it frees them of having to say the right thing!
Every piece of writing can actually start as a freewrite. Or how about just a conversation? When we are in conversation, we may say the wrong thing and then change our minds and correct ourselves. Conversation is so forgiving. We just change what we're saying in the moment. Easy.
So your job is to show your kids that it really is fine to say the wrong thing first in order to get to the right thing. You can do that by modeling it. Do freewriting with your kids and read aloud what you've written. Then make changes to yours, and let them see your thought process. Something like, "That's not really the word I mean here, maybe I should try this word instead." Look up the words in the dictionary to get the full meanings, so you can get it boiled down to the most accurate word choice.