I put the chicken and the vegetables on separate skewers. I also put the cherry tomatoes on a separate skewer from the zucchini, onions and green peppers. I start by putting the chicken on the grill because I like it burned around the edges. A few minutes later, the zucchini, onions and peppers. Finally the cherry tomatoes. This allow everything to cook at its own rate. Otherwise, your cherry tomatoes will be falling off the skewers before the onions are done.
I also use two skewers for each. That way things don't spin when you turn the skewer over.