I keep broodies and chicks separate from the flock until they are two weeks old, then they can go out with the rest. One of my broodies got tired of her chicks when they were around four weeks old. She just stopped mothering them and clucking for them.
They were lost and distraught at first, but stuck together as a group within the flock of older chickens. They made friends with two older chicks, and now the six of them hang out together. The older hens are tough on the younger chicks at roosting time- they push them off the roost if they get too close- but so far, no harm has been done. But my chickens have been selected for easy going temperaments, I won't tolerate a nasty hen or rooster, so your chick might not fare as well if your flock is more aggressive.