I routinely copy and paste text from Acrobat to any number of other Adobe CC applications (Illustrator, PS, InDesign). When I do this, it creates line breaks where they were visually represented on the pdf, meaning when pasted into a new doc there is no flow to the text.
Is there a way in any of the programs to clear this and "concatenate" the words back together into a flowing block?
You can't really get there in one step. Although InDesign could strip out the unwanted line breaks using a grep find/replace in some cases, that won't work at all for Ps or Ai.
The smoothest way to accomplish this is to export the PDF from Acrobat to Word, plain text or even Rich Text, or to use a converter like TextSoap (as Lauren recommends) or PDF2ID, from Recosoft, which does an almost magical job of creating editable, well-formatted InDesign documents from PDFs. (Their PDF2Office product does the same thing for MS Office Word, Excel and Powerpoint.)
Once you have text, you can copy and paste without the forced line breaks.