It's not called Kilz for nothing.

When it comes to general quick dry oil primers, Cover Stain is superior to Kilz

. Though strong, CS has lower odor, covers better, and is a bonding primer in addition to stain killer. Kilz

is not a bonding primer. If I have to carry one multi-use primer, it will cover stains
and bond, two uses I have need for on a regular basis.
OP's, do not use Kilz for your purpose. If it's pure vinyl wall covering, I guess that 123 will be okay, it won't penetrate. But, it will bond, and that's what you need, a primer that will bond to vinyl. Kilz

will not.
BTW, with all due respect armyfamily, if you think 18 dollars for a gallon of paint is high, you're out of touch. I see 18 as as close to free as I can get. How do you like all those as's?