I'm the PP that mentioned the TJ's fiber bars. We don't notice any digestive distress from them. But my kids won't eat the FiberOne fiber bars. Agree with PPs that berries and apples are also good sources of fiber.
There's also some good snack foods you can make that are pretty high fiber, like these:
http://www.howsweeteats.com/2012/09/quick-easy-no-bake-oatmeal-peanut-butter-bites/
or these:
http://www.rachaelray.com/2013/11/healthy-breakfast-cookies-for-kids (using bran cereal)
or these
http://www.thesneakychef.com/blog/2013/11/brown-sugar-breakfast-cookies.html
Here's a sample day's menu that has about 25 grams of fiber, which is what the doctors said we should shoot for for my son:
Breakfast:
Bowl of blueberries (5 g.)
White whole wheat toast (2 g)
Vegan sausage (1 g.)
Lunch
PBJ on white whole wheat (7 g)
Apple (4 g)
Snack:
Prunes, 1/2 cup (6 g)
Dinner:
Spaghetti w/ sauce and meatballs (1-2 g.)
I find that dinner is usually the tough time to get fiber in, for my family, because they don't really like whole wheat pasta or rolls. I usually aim for 5-10 grams at both breakfast and lunch, then 2-5 grams for snack and dinner.