Most problems are one of four things.
Check the kettle is on its base and plugged in, and that your phone is on the same Wi-Fi network as the kettle rather than a guest network or a different band your router treats separately.
On iPhone, the app needs permission to find devices on your local network. If you said no to that when asked, the app cannot see the kettle at all. Turn it back on in Settings, under the app's name.
If it still doesn't appear, you can type the kettle's address in by hand from the setup screen or from Settings. Your router's admin page will list it, usually as a device whose name starts with GD0.
Kettles get a new address when your router restarts. The app handles this by searching again, but if you typed the address in by hand it will be out of date. Use "Rediscover kettle" in Settings, or give the kettle a fixed address in your router settings so it never changes.
Press the Wi-Fi button on the kettle. Its light starts flashing and the kettle creates its own network called AK_Kettle. Join that network in your phone's Wi-Fi settings, then follow the setup screen in the app to hand over your home Wi-Fi details.
If your phone warns that AK_Kettle has no internet, choose to stay connected. Without that, the phone keeps using mobile data and the app can't reach the kettle.
The kettle refuses to start if there isn't enough water in it, and it doesn't explain why. Fill it past the MIN line and try again. The app warns you before this happens when it can see the water level is low.
The kettle only accepts one connection at a time, so another phone in the house has it. The app keeps checking and takes over by itself within a few seconds of the other phone going idle. Nothing to do but wait.
Email support@michaelhutchinson.me and say what the app showed you, what phone you have, and what the kettle was doing. It's one person answering, so replies may take a few days.