An absolutely excellent topic Barry!! and hope things are well there in the OK wing of the Smithsonian
I think the flammard was the way blade two hander of the landsknechts.
The flamberge term was apparently often misapplied to swords other than those with wavy blades, but generally refers to undulating blades on rapiers I believe.
There is a great deal of symbolism involved beyond any pragmatic application it would seem, and I have seen references suggesting that these blades were extremely difficult to sharpen etc.
As far as I have known most symbolism, at least in sword lore, is toward the 'flaming sword of paradise' from Genesis 3:24 in the Bible. In Freemasonry , according to Mackey (1873 &1878) this reference is used to describe the Tyler's sword of Masonic ceremony . While these were typically regarded as wavy, most Tyler's swords were of varied and celebrated forms.
The nagan or snake form as you have noted is well known in ethnographic forms, and many of the swords in India have blades like this . In Indonesia, the wavy blade of the keris is symbolically significant, and though unqualified to address this, I understand the number of waves (=luk) carry important meaning.
Returning to the European use of the wavy blade, it seems like the medieval to Renaissance use of these on two handers, and the use on a number of rapier blades were the most common instances.