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Without thread the gui is hanging and not scrollable and usable. Hence trying to introduce thread so that the gui does not hang ...
Then why does the OP talk of "But now I want this to be done in a 2-threaded mechanism, where every new connection should start a new thread to accept the data."? (Besides that saying "a 2-threaded mechanism" and "every new connection should start a thread" in the same sentence is very confused; and that the OP code showing nothing to do with Tk.)
You have a concurrent server which could be wrapped up into a function.
With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
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In reply to Re^3: How to introduce threading in socket communication