What is the possessive form of "y'all"?
It depends on whether you are indicating individual or group possession.
Did y'all get your coats?
Your is used because each person has a coat.
Is that y'all's house?
Y'all's is used because the house is theirs collectively. I never use y'alls's because y'all is already plural and doesn't need the s before the apostrophe.
For what it's worth, I'm from the Alabama and use both y'all and y'all's regularly.