You can run your app on devices registered to your (or your organizations) developer account using a development profile (most easily achieved by utilizing automatic signing - which requires xcode to be signed into your developer account). Then either flutter build ipa or using "Archive" and "Distribution app"/"Debugging" should give you an ipa package which you can then drag and drop on any registered device using Finder.

The procedure above is useful for distributing your app to other testers without the use of Testflight. Just make sure you are using a development profile containing all the devices the app is supposed to be tested on. Signing with a development certificate is sufficient then.