I think it's important not to discount the knowledge you have acquired through the years in regards to the printing process, the software and systems.
I was fortunate enough to be able to get out of the daily production aspects of printing, still be involved in the industry (which I love!) but gain new skills in a growing medium (web).
What specific skills did I learn in prepress that help with web design..not much. Some Photoshop and illustrator, even those have such different requirements not many skills cross from print design to web design. What has been a huge benefit is being able to work under tight deadlines, manage multiple projects and be flexible. All things I learned in prepress.
There are lots of small business that will have a need for a single person that can manage some print design, web work and social media. If you can get a good broad understanding of those 3, I think you could find a position outside of a prepress job.
Most web designers I have met don't know print. So I would take a stance that your print knowledge can put you at a huge advantage over some guy that just knows web design.
My opinion on flash: while it's good to know, look at how many sites today use flash compared to 5 years ago..almost none! It sucks for SEO, expensive to design, expensive to maintain and has limited mobile capabilities. I would put more focus on basic HTML, CSS and scripting.
Good Luck!