Use Quicktime instead
I have also had a lot of trouble trying to import movies into imovie 11, until I found that .flv files can easily be converted into .mov and .m4v with Quicktime.
Instal Perion and then open the .flv in Quicktime. Next, save the file with Save for Web. Once it is converted, right-click Open in Downloads. Go to Downloads and drag the file or folder to desktop. Open the folder and you'll find your movie clip automatically saved in formats readable by imovie. You can them import it into imovie.