I've had some "limited" experience in "moving" and modifying a "pre-built" Flash site, and it wasn't pretty, for me, because I know Flash only in passing. I'm not sure this will be of much help, but I will share with you my experience with that project, and maybe it will help you decide how to proceed.
You can't really just "hack away at it" the way you might when "deconstructing" a web page and have all the raw HTML out there in front of you to play with.
First, if you have the "original" Flash development files, you can open the "project" in Flash and modify the application as needed to accomplish your goal(s) on the new host. This presumes, of course, that you either have, or can acquire, enough knowledge of Flash authoring , and web development in general, to know what to change, and how to change it. I did not find this to be trivial. Becoming proficient enough in the Flash interface, and with actionscript, to do much of anything was very painful for me, and I have a "good" understanding of traditional web development processes. That said, from your description of your situation it appears that your goal is not "impossible"; it should just take someone profficient in Flash, and familiar enough with the Dreamhost maillist software (mailman, written in python) to replace the links to the appropriate software here on Dreamhost to get it to work.
If, on the other hand, you do not have the original flash project files (which is all too often the case when a flash site's developer is no longer with a project), the "wicket" get a whole lot "stickier". You will need to avail yourself of a Flash "decompiler", of which there are several for sale out on the web, to "decompile" the Flash files into something you can work with. I have no personal experience with them, and can not vouch for how well any of them work. Once that is done, you are back to the first situation.
Even though I have rather strong personal opinions about using Flash in general, and even stonger ones about entire websites in Flash (as both a developer and a user), they were not asked for in your post, so I'll refrain from expressing them here (unless asked to do so ). I'll just say that the situation you now find yourself in, taken as a whole, might be a good time to reconsider whether you want to try to maintain an "All Flash" website.
Many who have gone that road have, after the novelty wears off and the real issues with Flash sites begin to manifest themselves, ended up reverting their sites to more traditional/standard web technologies before they were faced with a "turning point" such as the one you now find yourself facing.
I wish I could offer you better help just "pointing you in the general direction", which I know is all I have done, but I don't have the knowledge of Flash required to do any better.
Given how long this post has been here, and what little response you have had, I am sure it would not be considered "double posting" to post this again, in the "Programming" forum, using a more descriptive subject line that is more likely to attract the attention of Flash enthusiasts and/or experts. Maybe something like "Requesting Help Modifying a Flash Site". You might also want to post the url to your site here, so others can see what they might be dealing with. Good luck, and I hope someone here is able to give you more useful help!