How do I measure genetic distance?
There are a few answers here, it is a little unclear which is closest to what you want.

[edited to be more complete and direct]

1) Nei's distance is mostly for comparing populations of the same species, so it should be fine if that is what you are doing. I am guessing that based on your post, you are more interested in cross-species comparisons. Of course, the logic is the same, it's just the math is different. For among-population divergence, Fst (fixation index) is also commonly used. But if you are using a sequence alignment or some such data to compute genetic distances, there are lots and lots of metrics. Some of them are very simple- for instance you could use Hamming distance and just count the number of residue differences between each sequence. 

As for computing these metrics, there is a webserver called GenePop online that will compute Fst for you if you plug in a dataset. I don't know of R packages that compute these things, I would guess just by looking at wikipedia that coding functions to do this would be relatively trivial (if you are comfortable with r).

2) If you are truly looking among species, a somewhat more appropriate approach might be to model your species in a phylogeny, rather than to use distance methods (though the two are attempting to solve sort of the same problem). There are lots of easy-to-use online programs for this, for instance: FastML. You can just copy-and-paste a seq alignment in there. After you have the tree in for instance newick format, there are good tools for visualizing trees both online at iTOL, and through R with APE. 

APE also has good utilities for modeling phylogenetic processes, so you could in principle directly model changes in protein folds through evolutionary time (assuming you have a meaningful summary of protein folding, either continuous or discrete).

I don't have enough reputation to link to more of the resources I mentioned, sorry.