Apparently there is no ready made integration between the Zello App and Flic as a Push To Talk (PTT) bluetooth button (as of 1/2019) for iOS.
If however you set within the Flic app the one click for example to represent the ”Global Music Controller” as toggle/play/pause, and you have the Zello app open, it will act as a PTT button just like the toggle button on your handfree headphones.
You might need to first press the Zello talk button on your mobile screen to give it priority but after that it should work fine. If however you should receive a phone call in between, the Flic app will default back to controlling music (in which case you need to reactivate the Zello again).
Why this is not already resolved by now I am not sure, I don’t need to controll my refrigerator with Flic but instead would appreciate a simple feature like this being more seamless.