Your situation presents some interesting challenges. Vent sexing newly hatched chicks is challenging. The hatcheries guarantee 90% accuracy so even the pros get it wrong a lot. That is only for full sized breeds. They won't even attempt bantams.
Sex links are not a breed. They are crosses. There are certain genes that a hen will pass on to only her sons. Her daughters will not get those genes. If those "sex-linked" genes she gives to her sons are dominant over the genes that the chicks get from their father, then, in certain cases, you can tell which sex the chick is at hatch. You have to have specific genes on both sides with no recessives hiding, but it is a pretty positive method. One example is the red sex link. The males are yellow and the females red or reddish at hatch, so you can tell them apart.
Wanting only 2 or 3 presents another challenge. Very few hatcheries will ship that few chicks. They usually ship a lot more so the chicks body heat will keep them warmer so they can survive shipping. Some will ship just a few, but they are very expensive due to the extra packaging and heat sources they ship with the chicks. If you are willing to spend the money, it can work. Your choice.
I don't know if you are dead set that you absolutely have to have baby chicks or would you settle for older chickens. It depends on the breeds but at 5 or 6 weeks old, you can sometimes tell sexes apart. For some breeds, you have to wait until later. The chickens will cost more individually, but you don't have to have a brooder and all the equipment for chicks. A lot of people sell Point of Lay (POL) pullets, somewhere around 16 to 18 weeks old. It might be something to consider.
You may be set on raising them from chicks. It can be a great experience for kids. You may be able to find someone local that will sell you some sex linked babies. Some people are willing to swap any that turn out to be roosters for pullets once that becomes clear, but you mentioned your son might form attachments, so I would stick with the sex links.
How do you find some local chicks or chickens? A few possibilities:
1. Advertise on here. Go to the Want to Buy/Sell section and put in an add. Read the rules beforehand but it is not that hard. You might get lucky.
2. Many states have threads in the Where am I./Where are You section on this forum. Do a search to find yours. If you post in that thread, you will often find somebody close by that will help you out.
3. Look through this link to maybe find somebody near you.
https://www.backyardchickens.com/forum/viewtopic.php?id=285981
4. Call your county extension agent and tell them what you want. They should be in the phone book under county government. They should know somebody in your area that can help you out.
5. Talk to people at the feed store. They probably know somebody that can help you if you get the right person. Or they might have a bulletin board you can post a notice explaining what you want.
6. It is the wrong time of year, but you can go to your county fair and talk to people showing chickens.
7. Look for chicken shows near you and talk to people there.
8. Many areas have chicken swaps. Suggestions 2 and 4 are ways to find these.
Im sure I am missing several possible ways to find chickens locally, whether sex link chicks or POL pullets. And there are other options, like splitting an order with somebody. Good luck however you decide to proceed.
