One thing I tell kids, mine and others I speak with, about writing is that there are two essential things you must do if you want to write well. 1. Write (duh) and 2. Read (not so duh).
When you write, it's like playing word catch with others. And, just as throwing the ball without catching it is only half the exercise (not to mention, really boring) writing without reading is only part of the story.
I read to get better at my craft, to stay informed about my profession, and for the pure enjoyment of it. And it's important to me that my kids see that. Last night we went to Barnes and Noble and everyone came away with something to read. Even Daddy. Then, when we got home, everyone picked a spot and dove into our books.
Read. What's more, let your kids see you read. Read to them, read alongside them. It not only makes them better communicators (which we need) it makes them more able critical thinkers (which was also need).