It looks like a huge, complex list, but there’s really only 5 sizes you need to build:
The first four sizes (listed in points) need 1×, 2× and 3× versions (if you’re being future proof, as well as covering the iPhone 6 Plus).
Some of the sizes you’ll see listed on the net and on Apple’s site are for iOS 6 and below (57×57 etc). They’re not needed if you’re targeting iOS 7 and above.
Here’s the Photoshop template I created:
I have slices set up to export each icon and an action to resize and reexport, so I end up with:
Not all those sizes are needed yet, but likely will be in the future. Starting with 4 base sizes makes building the icons far easier.
I’m using Slices in Photoshop to export the different regions needed for each icon. Please note that the icons you provide should not have any transparent areas — color should extend all the way into the corners. iOS will mask the icon, so you don’t have to worry about it.
You could do the same, using Affinity’s slice feature?
Update: I created some open source app icon templates for Affinity Designer, Sketch, Photoshop and Illustrator. They might be worth considering.