@Emil Thanks, I got it to work now. I had to open the flic app and execute the action manually from within the app. Then it will asks for Local Network permissions.
I checked the iOS settings before, but apparently the Local Network switch there only appears after it was requested within the app.

Since iOS 14 apps have to ask for permission if they want to access the local network. For that reason the current Flic app can't reach my Hue bridge anymore. Is there an ETA for an iOS 14 compatible app?