I have a flv player on my site, is it ok to use it to stream another site's FLV content since the site in question doesn't have any specific way to embed video?
Not without permission. If they don't offer a method of embedding onto another site, then they don't. My money is their content being restricted to only display on their website anyway.
I was able to get a working concept going, but didn't want to invest too much time into it if it was going to be highly frowned upon. The site does allow downloading of the flv's which is where I thought a gray area may exist.