What type of vinyl do you use?  

Naugahyde
It has been a few years since my last need, but I have had 2 chrome Lloyd lounge chairs recovered with Naugahyde. It seemed to be a good heavy, quality product. It has held up well.

another idea
Just remembered something else that might be of interest to you.
I had my chair pads recovered on my Heywood Wakefield dining chairs with new fabric a few years ago. I put thick(bought at an upholstery shop) clear vinyl over 2 of the chairs for the kids. They match, but are protected and you can remove the plastic down the road. The vinyl stretches and form fits very well.

All kinds
... of contemporary upholstery grade vinyl is available and most are great to use. I reupholstered the Saarinen side chars we use in our kitchen in vinyl (you know, kid and food) and it works perfectly.
Vinyl has come a long way and the stuff they make today, besides being very hard-wearing and economical has a great look and feel. Some is so convincing, it can be very hard to discern from leather. It's a great alternative in applications like we are talking about where leather or fabric would be damaged, and it's a good option where leather would be cost prohibitive. Plus if you are vegan it's animal free!
I'd talk to someone who sells upholstery fabrics or who works at an upholstery shop if you need some additional guidance.

maybe not
looked at an image of your chairs and they might not lend themselves to clear vinyl over fabric. Probably a tough edge to mess with more than once. They will be very cool freshened up with new vinyl!

.
as suggested...
go to prof'l furniture upholsterer, ask for manuf'rs extensive actual sample - it will show all product line, texture, pattern, color. Ask for larger sample of selected products, look at it under daylight then decide. While you're at it look at nauga, it looks right w/ some vintage furniture...

Picture
Here's a picture of the actual set.