Does Firefox for android support private browsing
Yes, it does. Go to Settings -> Privacy & Security and you can select there the option "Tell sites not to track me".
Hope that helps.
On desktop Firefox versions that setting only makes Firefox send a DNT=1 (do-not-track) header via the HTTP response headers and that has nothing to do with Private Browsing.
Neither of these things are private browsing. We are currently working on supporting this feature on Firefox for Android. I don't have a specific time frame for its inclusion at this time.