You then need to press the Bluetooth button on the Amazon Tap to start the Bluetooth pairing advertising process. Make sure you don't hold down the Bluetooth button to start the pairing process like in other Bluetooth devices, since that puts the Amazon Tap into a different setup mode.
In the LG G6's Bluetooth screen which you can get to by selecting Bluetooth in the main Settings screen, you should be able to see the Amazon Tap show up. If not, you will need to select 'Search' on the bottom of the Bluetooth screen. The Amazon Tap will then show up as a paired device and automatically connect.
You can easily select which Bluetooth audio device to play from by swiping down from the top of the LG G6 screen. Here you can select either the Amazon Tap or Sony MDR-XB950BT Extra Bass Bluetooth Headphones or even the LG G6's own speakers to play from.