The most common reason for getting a "169.254.x.x" address is that the adapter hasn't actually connected to the router to get its correct address. You don't say which version of Windows you're using, but have you 'scanned' for Available Wireless Networks, selected the one whose SSID (network name) matches that of your router and then selected the option to "Connect" to it? You would probably be prompted for an encryption key, which may be on a label on the underside of the router, and should then be connected.
What is Amazon Go and will it come to the UK? The store without checkouts or queues