Well, brace yourself.
I don't raise Cochin chicks any differently than any other chicks. Just make sure they have a clean brooder, fresh food and water available, and a heat source, and you're good to go.
They're on the slower side for maturity, generally around 8 months old at the earliest for laying. I would estimate they lay about 5 eggs per week per bird in their first year of laying, obviously less if they go broody. Their broodiness depends a lot on the line; one line I have goes broody and
never quits, another goes broody only occasionally, but at least once a year. They can cover a decent number of eggs, I'd say 8-10 depending on if they're bantam or large fowl eggs.
Fertility can be tricky. Sometimes the butt fluff just gets in the way. Trimming the fluff around their vents can help with that, though!
How well do they fly? My experience may not be best to say as most of mine are silkied, which means they fly even worse than a smooth-feathered Cochin would.

As youngsters they can fly decently well, but as they mature and fill in they are less able to jump as high and less able to get enough lift under their wings to propel them. Still, mine can get up ~2 feet high to hop up to their perch by themselves, so they aren't
totally incapable. They tend to do better with wider perches to sit on in my experience.
As for antics, goodness, where to start! They are the sassiest little fluffballs you'll ever know! Experts at giving the evil eye to the extent that even larger birds cower and flee. They aren't pushovers by any stretch. Bear in mind I have no true gamefowl so I couldn't tell you how well Cochins would handle themselves against them, but in a mixed flock of your average, egg layer or dual-purpose large fowl breeds, they hold their own. They can get sassy with me, too, but it always comes off as saving face for the rest of the flock. They don't want to damage their reputation with the other birds, you know? But if I'm sitting out there, they're perfectly happy to come over and sit in my lap, or they'll wait at my feet for me to pick them up.
Also, they have the cutest vocalizations! The girls are always 'baww-ACK?-ing' at me for my attention, and my boys like to go, 'bookity-bawww' in sort of a low tone. Their crows are adorable as well, sort of higher-pitched and with fewer syllables than the crow of larger breeds.
I especially love how interactive my boys are. Most other breeds I've had, the boys either don't want anything to do with me or they just want to fight me. The Cochin boys definitely go through a phase where they're kinda buttheads, but then they come out the other side of that and they're just the best. Chill, curious about me, tolerant of being handled. Here's Gus on my knee, for example, just checking in on what I was doing out there.
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Also nothing, I mean
nothing, is cuter than a brooder full of Cochin chickies in their fuzzy footsie pajamas.
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I think that covers about everything you were asking about, anyway.