The three complainants in the case - two women and a man - want the royal commission to examine why the Catholic Archbishop Philip Wilson has allowed Fr Fleming to resume ministry while the allegations against him are still the subject of an ongoing inquiry by the Anglican Professional Standards Office.
The Anglican investigation relates to Fr Fleming's alleged activities while he was an Anglican priest. It has been put on hold pending the outcome of a defamation case he has launched against the Sunday Mail for revealing the allegations in 2008.
The Catholic Church, which was aware of the nature of some of the allegations before it ordained him, allowed Fr Fleming to resume ministry in May of 2011, outraging the three alleged victims - who are identified only as Richard, Jane and Jenny.
Richard yesterday said he had contacted the royal commission secretariat asking to present a submission on the handling of his complaint.
"I am concerned about the process. The fact he has been allowed back into the ministry is unacceptable," he said. "I still have very real concerns he may escape censure because he jumped congregations. I don't know if the Anglicans can censure him."
Richard said he believed it "was clear the culture of the Catholic Church needed to change" as the diocese was aware of his case before ordaining him "yet they still took him in".
"The church clearly needs help from outside to make that change occur," he said.
Jane said she believed it was appropriate for the royal commission to examine the handling of the Fleming case.
"I have continually asked the question, how can anyone who is the subject of such an inquiry be put back to work in a church? His name has not been cleared," she said.