Going under the presumption you're displaying text within a SWF. How does it "get" into the swf? Via XML import or by importing a plain text file?
If it's a plain text file, line breaks/end of line characters between Windows and Unix/Linux are very different. So a simple "\n" in Windows may be interpreted as a "\r\n" when uploaded . . . my specific description may be incorrect but the concept is the same. It's not uncommon for, say, a Notepad document to be fine, then when uploaded and re-downloaded it comes back double spaced.
As mentioned a little more info will be required on how the text is brought in to Flash, you may just be able to do some replacement function to kill duplicate line returns.