The faction-based channel is global, game-wide, no matter what sector you're in. It chooses the correct channel for you based on your highest-ranking faction alliance, requiring a minimum of 3,000 faction points before you're able to get access.
To access this channel click the + sign in the chat window beside where you type and then select the faction channel that is available to you. Just like accessing the Help channel, you must have the faction chat enabled, to make sure you have it enabled click on the + sign then scroll up to Channels and make sure there is a check in the Faction, if you do not have the check simply click the box and it will place the check there. You will only have 1 option at a time and it will be the your highest/ most recent faction.
Note: If you have 2 factions that have the same faction points, then the system picks the most recent value that was changed. So if you are a Lightbearer and then get Enforcer to tie with it, you go to the Enforcer channel.