You can find the DesignatedRequirement and SigningIdentifier like this:
Start by installing the app on a device. On your Mac make sure you have the app downloaded in iTunes as well. In the folder "~/Music/Itunes/Mobile Applications/" you'll now find an .ipa file for you app.
Assuming that the app you want to target is "SomeApp" then copy SomeApp.ipa from that folder to a temporary folder. Rename the file and change the file extension from .ipa to .zip. Double-click to unzip the file. When unzipped you'll find that you have a folder named "Payload" in which a "SomeApp.app" folder exists.
Open a Terminal window and cd to the temporary folder. Run the following command:
codesign -d -r- "Payload/SomeApp.app"
This command will output the designated requirement ("anchor apple generic...").
Then run the following command:
codesign --display --verbose=1 "Payload/SomeApp.app"
This command will output a line starting with "Identifier=". The rest of the line is the SigningIdentifier.
Note that you mention the "App to Per App VPN" section of the linked manual - this specific payload is only supported on macOS. On iOS you do the same thing by sending the Settings command with an ApplicationAttributes entry over the MDM protocol.