Messed around with Flaux Nature a bit yesterday.
Duration seems to depend on how many stock of a current spell has been used. As for damage I couldn't really test anything since the training mode on cabinets is very limited and (to my knowledge, I can't read Japanese well) there is no damage display option.
For example :
1W/1A/1F - 3-4 in game seconds
2W/2A/2F - 5-7 in game seconds
3W/3A/3F - 9-12 in game seconds
Also with this, if you have a mixed spell up such as WFF (Rock), when used for Flaux Nature, the highest number element (in this case F) would get the buff. Whenever you have one stock of each (WAF) I believe (still need to test) the last element that hit will be the buffed option.
Hope this helps, I still have a whole lot to learn with her