Awww, Dawn, little Jack Jack is sooooo cute! I can see why you'd fall in love with him!
It's most likely that Jack Jack and Fin will get along, after the initial adjustment period, and I'm sure both the woman who runs that rescue -- her email is on the page -- and people here can give you tips for introducing the two. There are also products like Feliway that might help make the adjustment easier. I ran across a web page with a lot of good tips, too, a few weeks ago, searching for advice for someone else, and I'll see if I can find that again.
If by any chance they simply refuse to get along, most shelters will not only take the kitty back, but will insist on your returning the kitty to them rather than giving the kitty to someone else. You'll find out about this policy before being allowed to adopt, usually; it will be in the adoption agreement.
It's true that not all cats get along, but usually they will. I had three unrelated cats of different ages who lived together peacefully and happily for more than 11 years, with the oldest cat being with me five years before the younger ones were rescued, and the youngest one, Frosty, being with me until August of last year. (I still have to change the banner in my sig, which shows all three of them but hasn't been changed since Frosty went to Rainbow Bridge.)
I hope it's OK to link to memorial pages here. My memorial page for Tiger
has some pics of them together, as well as pics of Tiger and Frosty with the rescued parrot who came into our lives exactly two months before Sinbad left us.
You'll often see advice that if possible you should adopt two kittens at once, preferably littermates, and littermates will usually (not always) get along well throughout their lives. But my Frosty and Tiger were proof that unrelated kittens weeks apart in age, adopted weeks apart, can bond like littermates. And I've had friends with cats whose adopted kittens would bond that closely with older cats.
If you particularly want a kitty to keep Fin company, I'd recommend adopting one kitten now, rather than two. I was told by a feline vet I admire that usually two adopted kittens will play and bond with each other rather than any older cats in the household, and that was in a way what happened with my Sinbad and the kittens I rescued later, though she tolerated them well and sometimes played with them. But she was never so close to them that she would groom them or let them groom her (probably just as well considering her size and long coat). The kittens did groom each other, though. Fin's years younger than Sinbad was when I adopted more cats, so he's more likely to accept a new member of the family.
How will your dogs feel about a kitten? Have they ever been around a kitty that small? Many dogs like cats, and I've known of some that would mother small kittens, but each situation is unique.