I am not sure how knowing about the filing of conflict of interest statements by members of the board will help you understand conflicts between board members and senior staff.  Conflict of interest statements normally require disclosure of relationships that might involve economic benefit to directors stemming from economic transactions between them, their families, or their companies and the organization.  (See Ready Reference Page: “Conflict of Interest Policies Help Avoid Problems”) Conflict policies don’t normally deal with differences of opinion about the administration of the organization, which seems to be the basis for your question.

Conflict of interest statements are not normally open to the public, although the administration might be willing to confirm whether all members of the board have signed and filed conflict statements annually.  In your case, you would probably be better off to inquire directly about the conflict rumors that you have heard, asking whether they are true and whether you (and perhaps other docents) could be helpful in resolving the issues.  You may be told, perhaps more politely, that it is none of your damn business.  You may be told that there were issues in the past but everything is now copacetic.  It seems unlikely that you will be asked to help out with any problems that do exist.

If you don’t like the answer you receive, you will have to watch carefully to see if any of the rumored conflicts seem to be undermining the activities of the museum.  If the conflicts are hurting the museum, and you can’t do anything about it, you will have to determine whether your work helping visitors understand the collection is still worthwhile for the visitors — and for you.  As a volunteer, you are not required to continue if it isn’t.