Yes! Open the free or standard version (whichever you had) and sign up with FlightView to create a profile (tap Options button -> Settings -> Sign Up). Your trips in this version will be saved to this profile. Then open the elite version and log in--your trips will be downloaded to it. Go to the Trips tab and you will see them listed!
Also, if you are upgrading from the standard version of the app and use the in-app upgrade path, which can be found by tapping on More -> Upgrade to FlightView Elite, all of your trips and flights will be automatically transferred to the elite version.