Hopefully you have such a relationship and trust with your broker that you can ask that question of them. Most independent contractor agreements that I have reviewed, include the guidelines and/or policy regarding a sales associate selling their own property. You may also want to ask how you would be legally protected selling your own home, whether it be on your own or with the broker. Agents selling their primary residence are often excluded from the broker's legal protection.
You have the same property rights as anyone else. Yes you can FSBO your property. Just wright up a contract and hire an atty. or title company to close.
I have asked this same question.
Debra Albert, PA
Coldwell Banker Residential