add a little more breadcrumbs and another egg white.
your problem appears to be with relatively moist ground chicken and the veggies' cohesiveness.
all ground flesh combos, from italian meatballs, to swedish meatballs, to salisbury steaks, to kofta kebabs, to irish hamburgers have the intrinsic problem of the balance of meat, other ingredients, and moisture, with the eventual goal of being whiole but also tender .
too many chunky ingredients, especially when adding things like raw peppers or onions, chopped sundried tomatoes, fresh herbs, and so on to ground fowl makes for a crumbly mixture, so they will tend to fall apart. the quick solution is to saute the veggies first to help them reduce a bit, and balance the moisture with dry or wet ingredients.
the real trick is learning just how sticky the burger or meatball should be. adding egg whites is a moist ingredient but is also a good binder.
after the eggs, adding dry ingredients like breadcrumbs or grated cheese with ground chicken or turkey is a good way to start.
in my experience, it's best to make a somewhat dry mixture, then add a little milk to get the right consistency, or stickiness as it were.
for grilling, i would make them on the dry side, less moisture, rub the burger with a bit of oil, and s&p then plop then on a medium hot grill.
for meatballs and etc., they can be more sticky since they're frying in oil.