How far do I have to walk to hit level 10 Survival?

About 315 miles or so.

Method: Assuming Shawn Gordon's source is correct and you will have to walk for 30 hours to get to level 10, we can use that to figure out how far you have to walk. All we need is to figure out how fast Noctis walks and then to do a bit of math.

I parked my car at Coernix Station and then ran SW down the road so that I'd have a straight path free of obstacles to walk. Parking my car at the station gave me a marker with a distance on it. I walked until just after the marker ticked up to .35 miles, so that it wouldn't actually be .359 miles or something like that. (I'm assuming it rounds down.) I walked as straight and steadily as I could to the marker, and it took me almost exactly two minutes.

Multiplying .35 miles per 2 minutes against 1800 minutes in 30 hours gets us about 315 miles. It might be a bit more than this if I didn't walk perfectly straight, but it should be pretty close.