Your rankings could change but the fact that you currently have a flash site which most likely (without even knowing which site you are talking about) is poorly optimized with regards to on page content / seo, your ranking on Google is most likely based purely on incoming links. Chances are, if you properly code your site, utilize the correct header tags, keywords in your meta tags, keyword density on your pages... you may see better rankings than what you currently have.
Any time you make a change to your site, you could potentially cause your rankings to increase / decrease but again, in my experience Google seems to place so much value on your inbound links that even major redesigns of my sites kept me in the same position I was prior to the change.
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