It does look like FLAASH is removing the geo points from the input radiance file. It is not a real projection but FLAASH should not remove this information. What you can do is open the header of the radiance input image and copy the geo points structure, and then paste this into the header of the FLAASH result image. This structure will look something like this:
geo points = {
1.00000000, 1.00000000, 28.58157500, -82.75367300,
256.00000000, 1.00000000, 28.56729300, -82.66275500,
1.00000000, 3184.00000000, 27.71970400, -82.94301700,
256.00000000, 3184.00000000, 27.70551000, -82.85311700}
When you open the FLAASH file, you should have the pseudo projection back.
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