This is a great one for the kids, as we all know kids love anything on a stick. If the kids are wary of the herbs, leave them off and just do the chicken with maybe the garlic and lemon (if you really grate the garlic well it blends in with the chicken and they won't even know it's there!). If they're not big on onion (and let's face it - how many kids are?) you can use whichever vegetables they will eat, or just make the kebabs pure chicken, and serve them their veges on the side.
I would recommend serving with some sort of tasty dipping sauce (a lot of people like a Tzatziki style yoghurt dip with their Greek feast, but if you are dairy free maybe a herb pesto or a creamy tahini number would do the trick). Serve with a big Greek salad (lettuce, onions, olives, feta if you eat it, maybe some fresh mint and basil and loads of tomatoes), and you have a simple weeknight meal on the table in no time. Free of gluten, grains, dairy, nuts, soy, and sugar.