Hi my budgie just had three baby chicks and was wondering how long it will take for them to grow up and come out of the nest box.also what type of greens can they eat

Baby budgies will start to come out of the nesting box at about 4-5 weeks old, however will not be fully weaned until 6-8 weeks.
It is important to note that budgies left together to continually breed may lose the friendly nature that makes them good pets. They should not be allowed to breed more than once or twice at a time, then should be separated and reoriented to being handled and played with by humans.
Multiple breedings can also lead to low calcium levels in the female. You can use a cuttle bone to supplement.
Kale, spinach, the leafy green top of a carrot are good greens for parakeets, mine really like cucumber too.
Remember to remove the uneaten greens at the next feeding, bacteria can grow on them and be harmful to your birds.