To get back to the OP's original question: Can the small backyard flock owner make money on his or her flock? My answer below is based on the assumption that 1) you have a real desire to make money rather than lose it and explain away your loss, and 2) you have the intellectual discipline to do a real-world accounting of costs associated with production. If you're counting your labor costs at zero or ignoring the cost of land, taxes, or pen construction, you are not factoring in all the real costs of production.
Here's my answer: Yes, you can make money if you raise the right birds and target the right market.
The wrong birds to raise are any major commercial breed. The wrong market to target is the market for edible eggs. If you raise a common breed or sell eggs for the table, you cannot compete on price against the giant commercial producers, and
you are guaranteed to lose money, period.
If you raise high-value birds and reach out to the best markets (whether through
eBay, another auction site, web advertising, or whatever) you can make money. Once you build the infrastructure to produce chickens, the only difference between a breed that produces eggs worth 25¢ each or eggs that are worth $10 each is the acquisition costs of the breeding stock. It makes far more sense to buy the chickens that produce the $10 eggs. There are now many breeds in America --Orpingtons, Sussex, American gamefowl, tollbunt Polish, Onagadori, rare marans varieties, etc.-- where eggs routinely sell for that much, and chicks and pairs of birds sell for even more. In these markets you are not competing against giant commercial producers. In fact, because the birds you're selling are so rare, you're competing against almost nobody. There are 308 million Americans. Fifty million of them are on Facebook. 75,000 of them are on BYC. 147 million bidders are registered on
eBay. Somebody will buy a dozen eggs from you.
The good news is that not only can these breeds help you make money, they are also some of the most interesting breeds to keep. So, if you got into this because you really like chickens, you will be working with some of the rarest and most beautiful chicken breeds on the planet. That's a nice benefit. It will necessarily be part of your job to educate people on these rare breeds, and you will be doing those breeds a great service.