The Flight Master's Whistle is a nice way to get back to the closest Flight Master in The Broken Isles, but it's also possible to use on Argus. However, to use it on Argus you need 1 character that is revered or higher with the Argussian Reach faction. At revered you can buy the item Krokul Flute. This can be used to upgrade your Flight Master's Whistle to work on Argus as well as the Broken Shores.
Once you upgrade your whistle on one character, all other characters can also use the upgraded version on Argus. This was not the case on 7.3 launch, but was later patched in to make the game more alt-friendly.