Akaze descriptor from flipped image

I have a use case where I need Akaze to be flip invariant. I have seen this being done for SIFT in the paper “MAX-SIFT: FLIPPING INVARIANT DESCRIPTORS FOR WEB LOGO SEARCH” but I am locked into using Akaze for my application. I assume that flipping the image changes the order of elements in the (MLDB-Upright) descriptor? However, after a lot reading of the Akaze (opencv version) source code/playing around with test data I have not figured it out. Any ideas for figuring out the re-order??