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Update (2018-10-14): it is now possible to copy a box in the chat view by clicking on it. However, there is still no way to copy the entire chat at once.
It's currently not possible to copy text from the chat to the clipboard in BlueJeans on Microsoft Windows:
From the BlueJeans technical support on https://community.bluejeans.com/bluejeans/topics/would-like-to-be-able-to-capture-the-chats-after-the-call-ends:
Currently copy chat support with desktop app 2.0 is not available with windows machines. With the MAC machine it is supported. We do not have ETA for same. We will update the forum once implementation date is confirmed. Radhika Chatur.