Burning Suns can currently be enjoyed for free on the following platforms:
Tabletopia allows you to play Burning Suns in a 3D environment with complete freedom of movement and actions.
Tabletopia has a 2, 3 and 4 player setup which includes Terrans, Changelings, Templars, Cyborgs and Guardians.
Link to Burning Suns' Tabletopia Game Page
Vassal is a free open-source game engine for playing online adaptations of board games.
You can play Burning Suns either live on the internet or by email. Vassal runs on all platforms.
Link to the Burning Suns module on Vassal
Burning Suns also exists as a Zun Tzu Module, but it's currently out of date, as it's only a prototype - Link to BGG thread.