lol! The baby hasn't developed an arch yet because he's a BABY and hasn't even started walking yet! :) Babies even have baby fat on the soles of their feet. Shoot, my 2yo still has baby fat on the soles of his feet to a certain extent. That doesn't make him flat-footed. Don't borrow trouble from tomorrow. There is plenty of time to study his feet for signs of hereditary flat-feet later on when he starts taking normal child shape instead of baby shape.
As for the walker, as soon as they can sit up, they can use one....however, I really, really, really, really recommend a saucer instead for a few good reasons.
1. In a walker they can move around your home and reach what they normally couldn't. You don't want this yet. In a saucer, they can strengthen their legs without getting into trouble. They are stationary and easy to supervise.
2. Many people (some "experts" and pediatricians included) believe that walkers actually cause "walking confusion". This is when they are used to using their legs to move, but not in the way they would when walking, so it actually takes them longer to walk since they have to unlearn the bad habits that a walker taught them.
3. In a walker, they are scooting forward, but not really bearing their own weight or even maintaining their own balance so many people believe that the development of their leg muscles isn't as rapid if they use a walker whereas in a saucer, they are only bouncing up and down. The saucer keeps them from falling, but it doesn't help them move, so the only movement available to them is up and down, which they will discover and is very good for their legs.
I'm certainly no expert but I had both of my boys in saucers and they were both walking (or rather "running full tilt") at or right before 9mo. Since I didn't have any children in walkers, I have no basis for comparison except what I've occasionally seen with other people's kids, but I can't really comment on that since I wasn't a close observer; it was only a passing notice.