The most common reason for a majority of negative reflectance values in an image is an incorrect assumption of the units of the input radiance cube and the input scale factor to use in FLAASH. The scale factor that should be used is a value that when divided into the data cube results in units of uW/(cm^2*sr*um). You will need to confirm if your RapidEye data cube is already in these units. It sounds like the data is stored as integer so it is likely that a calibration to radiance or application of scale factors should be performed to get to the appropriate data units.