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I don't use flv so I,m not familiar with the tools for it. Most higher end consumer apps like Video Studio. should be able to do this with standard video. For free and with batch capability Virtual dub will fit the bill but I'm pretty sure it's not going to accept .flv but I may be mistaken. Haven't looked in many years and back in the day MPEG support had just arrived.
Detailed docs are available on the ffmpeg site. Basic command to add watermark image sampleimage.jpg to your samplevideo.avi:
ffmpeg -i samplevideo.avi -vhook "vhook\imlib2.dll -x ((W-w)-10) -y ((H-h)-10) -i sampleimage.jpg" -ar samplevideo_out.flv
This command places the image 10px from the right side, 10px from the bottom. Of course you can add path to all the three files involved.
Hope this helps.