Best games to play with kids are cooperative games: with small kids you can do all the job and let them just roll the dice or move figures and it is still great time (for all). Flash Point is great example of good coop to play with kids – I have played that with 3 and 4 year old. There is family variant and advanced variant if you want more challenge, you can also mix rules from both as you like.
I had high hopes for Flash Point Fire Rescue, wanted to play this with my kids as it is co-op game, fire-fighters co-op game. Well, it didn’t really work 😉 Older son (7) refuses to play any game if there is no fighting and hates each and every co-op game we have. Younger son (4) really likes to play it but we are limited to simplified family rules. Never played it with adults. There are few expansions available and base game cost around €30. If your kids are into cooperative games than this should work very well.