Frizzles and sizzles are not breeds of chickens so much as they are words describing three very showy feather types that chickens can exhibit.
Most pet chicken aficionados, for example, know what Silkies are. They are a breed of chicken with a feather type that is lacking in the barbicels that help the feather keep its tidy shape. So, silkie feathers end up looking very much like fur--and their feathers feel a lot like fur, too! The Silkie chicken breed is named after its feather type.
This White Silkie is showing off her unique feather type.
There are other unusual feather types called sizzle, frizzle, and frazzle, and they don't (at the time of this writing) have a breed named after their feather types.
A frizzled feather essentially curls outward, giving the chicken a charmingly windblown look. Compare the feather types of these hens:
A smooth-feathered Serama hen (on the right) next to a frizzled Serama hen (on the left).
They are both Seramas; however, one has frizzled feathers. For short, sometimes birds with these feathers are called "Frizzles." Remember, though, a frizzle is not a specific breed. You might have frizzled Seramas (as above), frizzled Polish, frizzled Cochins, and more. Even though they're all different breeds, they can collectively be called frizzles.
The other feather type, "sizzle," combines "silkie" and "frizzle" feather types. So, not only are the feathers lacking in barbicles--so they have a furry appearance--but they're also curled out and windblown.
What a cute Sizzle rooster!
Well, since sizzles and frizzles are SO fun and funky, how come we don't see more of them?
The answer to that is that the breeding is complicated, because frizzles are complicated. Birds with two frizzling genes are called "frazzles." TWO copies of the frizzling gene can produce problems like an enlarged heart, in addition to poor feather quality produced by doubling those genes. So frizzles don't breed true, and never will. Responsible breeders cross a frizzle with a smooth feathered bird to get 50% frizzles, and no frazzles.
Silkie feather genes, by contrast, are not problematic in that way; two copies express as silkied feathers and so does one copy. Silkies can breed true because they can have two copies of the gene without that gene creating fatal complications for the offspring. But when you outcross Silkies (adding new genetic material to the line to increase genetic diversity and improve the breed), even though the 1st generation offspring may get silkie feathers, the 2nd generation still has a 25% chance for non-silkied feathering.
Essentially, juggling silkying genes and frizzling genes at the same time--trying to get just the right combination to be able to produce a sizzle--is difficult work that not all breeders are willing to do. Over a few generations, you have to breed in the silkying genes and breed out the recessive smooth feathering, while also making sure to be responsible and not producing frazzles.
The bottom line is that if you love sizzles they can be difficult to find, and you always want to make sure you purchase these breeds from responsible breeders to ensure the health of your flock.