Vine Question

HI! I thought this might be the forum to post this on:
I'm looking for a flowering vine to plant on the chain link fence around our dog kennel for next year-need something that is not poisonous . I've read that the seeds of morning glory and hyacinth bean are both poisonous,( DH wouldn't like it if I killed his beagles! :) and those dogs will eat anything that lands in the kennel so...............................

Can you give me some ideas so I know what to look for?
Thanks for any help!

I have runner beans around my chicken coop. They grow fast and get a pretty flower.