Problems with

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sending a line every loop is a total overkill. Better use some pauses in this test.
the server side:
fsUDP = CreateUDPStream(23456)
SendUDPMsg(fsUDP,DotToInt%("84.61.21.241"))
While Not KeyHit(1)
 WriteLine(fsUDP,Input$("")
Wend

doesn't make sense. Instead use
fsUDP = CreateUDPStream(23456)
While Not KeyHit(1)
 WriteLine(fsUDP,Input$("")
 SendUDPMsg(fsUDP,DotToInt%("84.61.21.241"))
 delay 1000
Wend
closeudpstream (fsUDP)


And the client part has a little typo:
If RecvUDPMsg(fsUDP) Then
 Print ReadLine$(fsUD) ; <<<<<< use an existing stream
EndIf


Basicly I'd suggest to use ReadAvail(stream) and Readbytes instead. it won't wait for a linefeed. And for local test on one machine use localhost (127.0.0.1).