The typical issue when this sort of thing happens is the Path. When you test your Flash file, and the SWF and the FLV are in the same folder, you don't need any path info, just the FLV name, since they are in the same folder. But when you're running the SWF from an HTML page, the path in the SWF needs to be the path to the FLV from the HTML, not necessarily the SWF. If the FLV, SWF, and HTML files are all in the same folder it should still be OK, but typically the HTML is calling to the SWF in another folder, so be sure that your FLA has the path to the FLV from the HTML location.
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