I have uploaded a flv and a jpg image into a album folder. Both the video and jplayer plugin has been enabled. However, the video won't play, even there's an image thumbnail.

Maybe the flv is not created correctly or your browser has no supported flash player.

Visited your site quickly. This is a theme problem. The theme displays the images via a script named Galleriffic which is not the standard theme way and conflicts with the (any) video player (script within script issue). There is no easy way around that. Since that gallerffic script is not compatible with the current Zenphoto - gallerffic has been abandoned by its developer years ago - you probably are on an older Zenphoto version additionally.

I am not that familiar with the theme but if available choose another display way for the videos.

That is Zpardiose which I believe is currently maintained. However as acrylian says videos cannot be displayed directly in gallerriffic.

So how do I make it work?

Simple answer: If the theme has no display mode without galleriffic you can't. Then you have to use another theme.

Even I used the basic theme, I couldn't get the video work. Anything I missed? Or any plugins that I need to enable besides video, jplayer

You said above you use a flv file. If that is not working there are several possibilities:

• The flv is not created correctly. It is a container that can contain numerous codecs but to work with Flash there are some requirements (depending on the Flash player version)
• You don't have Flash properly installed in your browser or not the right version
• You are using an iOS device (iPhone, iPad) which does not support Flash

It is recommended to use mp4.

Please see also here which browser supports what (this is not jPlayer specific generally):
http://jplayer.org/latest/developer-guide/#reference-html5-media
http://mediaelementjs.com/#installation (another player, scroll down to a similar, but better table overview)