Your example indicates that 'diaspora' might be the appropriate word:
2. In extended use. Any group of people who have spread or become dispersed beyond their traditional homeland or point of origin; the dispersion or spread of a group of people in this way; an instance of this. Also: the countries and places inhabited by such a group, regarded collectively.
3. The state or fact of having been dispersed from one's homeland or point of origin.
In your example, 'diaspora' fits:
Consecutive droughts led to the diaspora of natives to other regions in search of greener pastures.
I suppose you could stretch the point, but in your example sentence, diffluence seems wrong to me. This is because diffluence refers to 'dispersal by flowing'. While you could say figuratively that the natives are flowing to other areas, it seems to be an unnecessary and possibly awkward figurative reach when more apt terms exist.
If you want a less ponderous (and more general) word, 'dispersal' or 'dispersion' would also work:
1. The action of dispersing or scattering abroad; the condition or state of being dispersed; scattering, distribution, circulation.
(All definitions from OED Online.)
So, thus in your example:
Consecutive droughts led to the dispersal of natives to other regions in search of greener pastures.