First off, Great job Brian and Caught108.
I have two teenage boys (18 and 16), and unfortunately I have not been able to completely get them addicted to flyfishing (yet). There are so many other distractions that provide easier and more instant mastery that some kids just never will get interested in the concept of flyfishing, on its own. To me, the more important effort is to get them out of the house and into nature first and then concentrate on fishing and eventually flyfishing. Luckily, after spending way too much time travelling to play hockey between the ages of 8 and 16, with two years of effort I have been able to get my oldest son very interested in nature. In fact, next week we are going to SW Colorado to Backpack and fish for 10 days in the South San Juan Wilderness. My younger son unfortunately, is still not into it (yet), hopefully that will change.
More than age, I believe that your relationship with your kids will dictate if they will give flyfishing a real shot. Some kids want to emulate their parents and really want to do everything they can to impress them (these will be the easiest to get started), while others are more rebellious and want to be more contrarian.
If they want to emulate you, I think you could start in the 6-8 year old range (as you Brian have pointed out is when you started and then fell in love with it once you start seeing some tangible results). It will be important for them to catch fish because if its too hard, they will lose interest. Pond fishing for bluegill is a great way to start learning and getting kids excited.
The outdoor experience is important too. Camping and hiking can be a great way to get them interested in the outdoors. You have to make it fun and you can't make it too strenuous, after all you don't want them to dread being outdoors. One thing my boys really liked doing in the park was looking for salamanders and lizards (and snakes!!). You can incorporate all sorts of things into trips to the stream. And of course, being a responsible steward of our resources. Picking up trash that someone else dropped can have a profound impact on a youngster.
Here is a book that I purchased a few year back to provide some insight on teaching kids to flyfish, it might provide some useful insights, as well:
Keep up the good work and don't lose faith. You'll need lots of patience, but watching your child catch fish is alot more fun than catching them yourself! Make sure you get a picture of them when they catch their first fish. If you can, save the fly that they used, it makes for a great piece of family history to have the fly that they used to catch their first fish with...