Hello ewheat22,
We understand you have an option for a specific app to access your local network, but you don't see this option on another iPhone. We also understand you've uninstalled and reinstalled the same app on the iPhone that doesn't have this option, but the app still doesn't ask for permission to access Location Services, which appears to be necessary for the app to work correctly.
To determine if this is a setting on the iPhone or the app itself, we'd recommend reviewing the location settings for the app in question. You can read more About privacy and Location Services in iOS and iPadOS.
Since you mentioned this specific app including local network as an option for app permissions, Location Services may need to be enabled for the app to work properly. Please see how to Turn Location Services and GPS on or off on your iPhone, iPad, or iPod touch for additional details.
If the option still doesn't display for this specific app, please make sure Screen Time isn't restricting the settings on the iPhone that doesn't see this option. For additional details on Content & Privacy Restrictions in Screen Time, please see how to Use parental controls on your child's iPhone, iPad, or iPod touch.
If this option still isn't available after confirming Location Services is enabled, and you've ruled out any type of Content & Privacy Restrictions, we'd recommend making sure both iPhones are using the latest version of iOS. We've recently released iOS version 14.5.1. If an update is needed, please be sure to create a current backup prior to updating. We'd also recommend checking for app updates. These links can help:
If this option still isn't available for this specific app, please let us know which app you're using.
If the iPhone and all other apps appear to be working as expected, you can also contact the app developer. If needed, please see How to contact an app developer.
Cheers!