As @txnelson commented, there is no test option natively in JMP currently (as of 17.0.0) for a "multiple comparison's version" of a test for Unequal Variances. You can certainly do the variance comparisons separately pairwise, but you won't get the benefit of alpha correction like you do with a multiple comparisons test on the means with a method like Tukey-HSD.
I'd recommend searching the Wishlist and putting this one on there (community.jmp.com/wishlist) if it's not there already.
Note that in JMP 17 in Oneway, you now get a plot of the 2-sided confidence interval of the standard deviation by Level, vs the overall average standard deviation (dashed black line). This is meant to give you a graphical-visual indication of where the variance might be different between levels (relative to the grand average standard deviation).
![PatrickGiuliano_0-1673957330458.png PatrickGiuliano_0-1673957330458.png](https://community.jmp.com/t5/image/serverpage/image-id/49174i841798A488319E7A/image-size/medium?v=v2&px=400)
You can also use Analysis of Means (ANOM) Methods (e.g. ANOM for Variances under the red triangle in Oneway), or Heterogeneity of Variance (HOV) testing (in the Variability/Gauge Chart Platform) to help explore/ identify where specific variances are not the same between groups.