OK, here's what I would do.
Either buy spray or regular Kilz, either will work.
Paint your chair with a matte finish outdoor latex paint in the main color you want the chair.
Then add the designs or the finishing touches with one of the outdoor acrylic paints, which I think only comes in gloss, not sure, but the gloss is ok for the design work.
Gloss paint sort of rejects any other kind of paint that's applied to it, the matte or satin finish doesn't. But if the gloss is on top of the other layers it won't have anything else over it. I think you are safe if you use outdoor paints anyway and you should be able to get them at a hardware shop in the colors you need.
Here's what I use, but mostly for indoor things. Even so, this will also work for exterior. I was just thinking you might be able to find what you want in small cans at a hardware store. You should be aware of its base, though. Paints with an oil base won't hold acrylic/latex over it very well. Acrylic/latex is water based, it just doesn't adhere to oil.