HE is using it to initiate contact so, quite possibly he is flirting, yes. Is she flirting with him? uncertain
You guys talk all the time on here about reaching out and touching 'to see' how she reacts. If she doesn't recoil, that is a good sign. I agree with this philosophy/perception. Myself, I dont touch people that I dont want to touch and will recoil if someone tries to touch me when I dont want them to.
So, let's turn that around. Instead of him reaching out to touch, he invites her to touch. He is basically testing the waters to see if she is physically open to him, on some level.
Do I consider it flirting? No. could it be considered as a means for him to test the waters as far as her being open to him? yes. If she touches him does that means she cold be interested on some level? That's quite a stretch.
If neither of them are otherwise engaged romantically, and he is interested, he should see if he can progress things.