I am active on a site that is predominately about user supplied content. Users can upload content with little restriction, and the for profit backers manage most of it with paid staff. Often spam can live on the site for several days if staff are busy with income generating issues, while there is a spam notice flag that allows users to report spam there does not seem to be an automatic hide feature as is present in sites like Stack Exchange and Craig's list.
You need to show two things:
That having the spam visible on the site is hurting their revenue.
That users can be trusted to flag responsibly.
Both of these are going to be difficult to achieve without the support of someone within the organisation - you need figures to show that people are turning away from the site because of the spam and you need the site to develop the flagging system and the checks that go with it to ensure that flags are reviewed both by the rest of the community and by the admin team.
This isn't to say you shouldn't try - you can point to sites like Stack Exchange where it works well and have the required checks:
- Multiple flags from different users are required to automatically remove a post.
- The flags are recorded so that they can be reviewed by admins to ensure that they aren't being misused.
- There is a mechanism to challenge the flag (meta or contacting the team).
I have seen comments elsewhere on the web that praise Stack Exchange for it's lack of spam - so we must be doing something right.
Ultimately though it's the first thing that will tip the balance. If having spam hanging around isn't hurting the company's bottom line then there's no pressure for them to do anything about removing it.