How can I mount a screen window to an old porch?
I'd say mount it on the outer part, like @JACK suggested. Otherwise you'll probably end up with some odd-looking custom bracket/track setup to accomplish what you're after.
Instead of the stud screw + wingnut combo though, they make screen clips that match the color and width of that screen kit you linked, which might look a little cleaner. Below is a plastic one (I only searched Home Depot though, so you may find metal ones elsewhere, if that's what you're looking for).

Screen Clip
  

It might be worth investing in stainless steel screws (I didn't see what material the included screws were, but I kinda doubt they're SS), but at $0.30 per clip it doesn't hurt to try.