If you allow port 80 and 443 access out of your network then accessing the Apple App Store from behind your firewall it’s a doddle.

However if you have a more locked down area of a network but have iPads etc that need App Store access here’s what you need to allow port 80 and 443 access to:

17.154.0.0/16 Apple's Class B Subnet includes phobos.apple.com address(es)
23.63.98.0/23 Akamai Technologies CDN

I appreciate this is a bit of a wide range of addresses, but unless you want to be having to packet capture and analyze where the App store is heading too that week it’s a reasonable. I doubt anyone would give up a class B IPv4 range nowadays.

Hope that helps some of you out!