1st Solution
Note that this code will only be valid for the current video/clip playing. You would have to sniff out the stream again for other videos or clips you'd like to record/download.
Code:
rtmpdump -r "rtmp://204.77.214.17/mogulus-stream-edge/wilsonjj" -a "mogulus-stream-edge/wilsonjj" -f "WIN 16,0,0,235" -W "http://cdn.livestream.com/chromelessPlayer/v21/playerapi.swf" -p "http://www.livestream.com/embed/wilsonjj?showMoreVideos=false&hideInfo=true&autoPlay=true&lschannel=true&browseMode=false&textLines=2&hideChannelBranding=true&mode=false&allowchat=false&layout=4&t=519283" -y "rtmp://212-94.livestream.com/affiliateStream/wilsonjj/6c69766572657065617465723a72746d703a2f2f3231322d39342e6c69766573747265616d2e636f6d2f6d6f67756c75732f77696c736f6e6a6a2f6c69766573747265616d" -o "2015-01-05_12-06-03_va07092.flv"
Code:
c:\>rtmpdump -r "rtmp://204.77.214.17/mogulus-stream-edge/wilsonjj" -a "mogulus-
stream-edge/wilsonjj" -f "WIN 16,0,0,235" -W "http://cdn.livestream.com/chromele
ssPlayer/v21/playerapi.swf" -p "http://www.livestream.com/embed/wilsonjj?showMor
eVideos=false&hideInfo=true&autoPlay=true&lschannel=true&browseMode=false&textLi
nes=2&hideChannelBranding=true&mode=false&allowchat=false&layout=4&t=519283" -y
"rtmp://212-94.livestream.com/affiliateStream/wilsonjj/6c69766572657065617465723
a72746d703a2f2f3231322d39342e6c69766573747265616d2e636f6d2f6d6f67756c75732f77696
c736f6e6a6a2f6c69766573747265616d" -o "2015-01-05_12-06-03_va07092.flv"
RTMPDump v2.4
(c) 2010 Andrej Stepanchuk, Howard Chu, The Flvstreamer Team; license: GPL
Connecting ...
INFO: Connected...
Starting download at: 0.000 kB
INFO: Metadata:
INFO: duration 0.00
INFO: fileSize 0.00
INFO: width 512.00
INFO: height 288.00
INFO: videocodecid avc1
INFO: videodatarate 436.00
INFO: framerate 25.00
INFO: audiocodecid mp4a
INFO: audiodatarate 64.00
INFO: audiosamplerate 44100.00
INFO: audiosamplesize 16.00
INFO: audiochannels 2.00
INFO: stereo TRUE
INFO: encoder Open Broadcaster Software v0.638b
INFO: lsChannelName wilsonjj
2019.104 kB / 42.54 sec
Caught signal: 2, cleaning up, just a second...
2023.015 kB / 42.58 sec
Download may be incomplete (downloaded about 0.00%), try resuming
Terminate batch job (Y/N)?
2nd Solution --well not really coz the video you end-up with has some weird resolution 
You can try using Livestreamer...
Code:
livestreamer --http-no-ssl-verify "http://www.livestream.com/wilsonjj" best -o JapClip.flv
Code:
Microsoft Windows [Version 6.2.9200]
(c) 2012 Microsoft Corporation. All rights reserved.
c:\livestreamer>livestreamer --http-no-ssl-verify "http://www.livestream.com/wilsonjj" best -o JapClip.flv
[cli][info] Found matching plugin oldlivestream for URL http://www.livestream.com/wilsonjj
[cli][info] Available streams: 0, 250k (worst, best)
[cli][info] Opening stream: 250k (hls)
Written 1390072 bytes
P.S. I'm sure some livestreamer experts on this forum can suggest additional commands/parameters to fix/adjust the resolution...
Cheers!