I'm pretty new to chickens so I could be wrong, but here is my experience. I got 3 chicks when they were three days old. The other day I got seven more that were the same age, six days old, but from a different place. I put the seven new ones in with the three existing chicks and they are all fine. They huddled up together and I have had no issues. They are now 8 days old.
give them a day or two to strengthen thier legs and get used to being a chicken, then they should be fine. last fall i had a very staggered hatch under a broody. when they first chick hatched i put the eggs under a different broody, leaving the one chick with mama. when the next chick hatched i let it recover under a heat lamp, then moved it. the rest of the chicks hatched over the course of about a week and even with that much difference in age they could all keep up fine.
i love this photo. the black chick was less than 24 hours old, the yellow chick was about 3 days and the biggest chick was over a week. of course being half serama, the black chick was pretty teensy. he had a protien deficiency (i think) which caused his first feathers to be very brittle with pale sections that grew when the deficiency was at it's worst. i was scared we wasn't going to make it, but he's doing great now. the hatch was all cockerels but one, so i kept only him and the pullet to put in my silkie and serama coop.
This may not work with strongly game chicks or ones with a lot of game heritage like Cornish.
But, you can often add new chicks with existing chicks, up to a week apart. This is the way I hatch and raise batches of chicks - I generally add 2-4 eggs to the incubator 2 days to a week apart, marking each egg with a number and then writing it down on the calendar. They then hatch in a staggered pattern, and every few days I'm adding new chicks to the brooder, in with existing chicks. This works for about a maximum of one month. The oldest chicks get so accustomed to new chicks arriving every few days that they do not pick on them as much, if at all. I also use a red heat lamp to discourage picking.
I use a separate incubator for hatching; this would not work very well otherwise.