No, I am not aware of any formal measure of intersectionality.  This is usually approached in typical crosstabulation/correlation fashion quantitatively, and strategically qualitatively.

I appreciate your answer and I have come across measures for diversity (several indices) but no formal measure of intersectionality or knowledge of intersectionality.  Are you aware of any qualitative measures?

What a great question...I'll be following this to see what answers you derive.  This is somewhat outside the parameter of your question, but it seems that the medical community has developed excellent tracking for disease management that might have useful application for intersectionality. There could also be some application with social network analysis (though its methods are quantitative). 

I am not familiar with a specific tool or index myself. However, Professor Olena Hankivsky has written a great deal on intersectionality as a policy tool. A search for articles and white papers authored by her seems a good place to start.  And if that search is unproductive, perhaps try contacting her directly. I believe she is affiliated with Simon Fraser University, British Columbia, Canada. 

Michael,

Very good question.

I developed a technique when I wanted to study the role of ethnocentricity in accented speech. I realized that with sensitive issues there is something more at stake than the classical Labovian observer's paradox or the researcher's bias. Something inherent with the subject itself which may be called the subject paradox.

Anyway, I first used priming and made my subjects not aware of the intentions behind my questions. Then I made a Derridean deconstruction ( the presence that hides absence) of the results I found. But I did not stop there, I wanted to reconstruct the absence ( my results) and see if  I can find similar results ( similar presence). For this reason the subjects of my study were the best help. Instead of priming,  I asked  direct questions linked with the results ( absence) of my findings.

This heterogeneous triangulation is to my mind valid and reliable. Take care