Diagnosis
The camera is stuck in its pairing/sync mode. A flashing amber light means it's looking for a connection but can't find your network or phone.
How to Fix It
Force a fresh start. Hold down the sync button on the camera (it's on the bottom, near the power port) for about 15 seconds until you see the light flash amber rapidly, then release. The camera will reboot. Now, delete the device from your Arlo app completely and start the "Add New Device" process over from scratch, making sure your phone's Bluetooth is on.
If That Didn't Work
Your phone might be connected to your WiFi's 5GHz band. The Arlo Baby setup requires your phone to be on the same 2.4GHz network as the camera will use. Go into your phone's WiFi settings and manually connect to the 2.4GHz band of your network before trying setup again.
Heads Up
During setup, keep your phone very close to the camera (like within 3 feet). The initial handshake uses Bluetooth, and it's surprisingly short-range.