I have been using photoshop and saving as pdf an then using flexi version 12 I believe it is.
I would start by using a High quality JPG or a TIFF format with RGB colorspace. Is your monitor profiled? And how accurate is that profile? That will make a difference as well.
Then, besides the profile, there are a number of RIP settings that can make a difference. And a canned profile will never outperform a customer profile built on your RIP, RIP settings, printer, media in your environment. Until you're ready to make the investment in custom profiles, you're going to have to do a lot of experimenting till you get what you want for that picture. And the next picture may take different settings, so you may have to start all over again. There should be a tab in RIP and Print, or it may be once you have the job in production manager where you can tweak the colors.
Another trick is to open up the file directly into production manager, bypassing the design side of Flexi.
Good Luck