Usually rendering a movie as a SWF file is not a good choice. And Vegas doesn't do it.
Is someone requiring you to deliver a movie in a SWF file? If you're not being forced down this route then the better route is probably going to be to encode an MP4 file from Vegas. This would give you more player options, including the option of a SWF file loading and playing the MP4.
SWF itself is a kind of programmable animation file. While you can embed video into it the better practice is for the swf file to call, load, and play an external video file. This is what most/all prepackaged Flash Video players do. Embedding video directly in a SWF forces a 16,000 frame limit on you and the swf cannot retain sync between sound and picture, so it's usually not a great choice.