How much duplication is permissible in letters of recommendation?
While our university occasionally submits statements of purpose, research statements, and writing samples through plagiarism detectors (and gives the admissions committee the results), I have never seen this done to letters of recommendation.

There are just very limited ways of saying nice things about students. I use the same variation of an opening for all my letters, with only minor changes in intensity (I am very/slightly/marginally pleased to write this letter of recommendation) and close with the same sentence on all of them. 

I wouldn't worry.



Addendum given the changes to the the original question: I don't know if people have seen the output of plagiarism detectors but they don't provide  a simple YES/NO answer. Instead, they provide a statistical quantification of how much unquoted text might be drawn from other sources (e.g., 3-5% of the text appears duplicative). Each report is several pages long with parts of the student text highlighted and possible prior sources highlighted. 

The reports are quite "noisy" with many false positives -- notably in one case that I remember, highlighting text in the bibliography because the citations matched citations in other bibliographies. [facepalm] 

Running LORs through plagiarism detectors would serve no useful evaluative purpose in terms of how the admissions committee views the candidate.