Unfortunately many law enforcement agencies are not eager to prosecute, or perhaps don’t have the people power to prosecute, minor crimes.  You have not said that your nephew has actually raised funds that he hasn’t returned to you, even though you may be suspicious because of his history, so the FBI may not want to investigate the situation as a crime.  Because you can’t get the FBI interested, however, doesn’t mean you should go to the Better Business Bureau.

If your nephew won’t stop after a specific request (and you can’t get sufficient help from your family), I would work with the charitable solicitation registration office in the state in which he is soliciting without your permission.  (You want to be sure that your organization is registered in that state if required to do so.)  Even if you are so church-related that you are excluded from the registration requirement, most state charitable solicitation laws prohibit anyone from soliciting in the name of charity without permission to do so.  They also prohibit the solicitor from making other misrepresentations in connection with the solicitations.  The state could probably enjoin his unauthorized solicitation.

If the state is not responsive, you could bring your own private action to enjoin him from soliciting for you.  You could do either of these things without revealing his alleged drug addiction, simply on the basis that you don’t want him representing you.  The private action could be expensive and time-consuming, but is likely to be ultimately successful if you are willing to pursue it.