Yes, you do need a Flair Puck. Every Flair system needs at least one Puck, configured as a Gateway and plugged into power using the supplied cable and adapter. This "Gateway Puck" is connected to your home WiFI and acts as a communication hub for all your other Flair devices (even if you only have one Puck in your system).
A Puck comes out of the box as Sensor Puck and gets configured as a Gateway during app Setup, so you don't need to buy anything special.
Gateway Pucks can read temperature, too! So you can use them in rooms with Smart Vents or to control a mini split, window AC or portable.