I don't believe this is a conflict of interest. The REA is contracted to get the best deal possible for the Vendor, being the same person does not preclude this. They cannot work as a BA for their own property however as that is working both sides of the transaction.
According to a price finder report I ran this week I have seen a REA selling his own property in Perth.
Yep, of course the agent can sell their own property (but note 'agents interest'). It is more common for the agent to fob it off to one of their sales crew as even agents are too involved in their own house to be objective.