I'm pretty sure pintos are a bush bean Mike, so not much of a privacy screen from them. But you could certainly grow a pole bean variety on chain link.
Welcome to TEG @crazzzymike13 !!!!!!! I grow green beans that have become almost famous on this site. Here is a link to the thread about them. They are Thai #3 Long Beans from www.rareseeds.com
We've got at least two bean aficionados on this forum, Mike. I bet @marshallsmyth or @Bluejay77 would be able to recommend a climbing pinto type bean. Maybe they will see this and add their 2 cents worth.
How could I forget? @Bluejay77 did his free beans grow out last year and promises to do it again this year, in April. You select bean seeds, he sends you seed, you grow the beans, double the number of seeds and send them back to him. He is a bean collector and does not have the room to grow all his varieties, so we help him refresh his seeds. In return, we get a chance to have some awesome heritage bean varieties.