What is the established antonym for "confluent"?

Your example indicates that 'diaspora' might be the appropriate word:

diaspora, n.
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:

dispersion, n.
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.

Diffluent is a less common term compared to confluent, but it is used especially in scientific/formal contexts:

• Flowing apart or off; dissolving; not fixed. (TFD)

Usage Example:

• Confluent and/or diffluent wind patterns were observed in echo bands in all quadrants and at different elevations in the area around the radar. (Cloud Dynamics: Proceedings of a Symposium held at the Third ...)

Ngram: diffluent.

As per your update I'd suggest migration:

• Movement of people to a new area or country in order to find work or better living conditions: the extensive rural-to-urban migration has created a severe housing shortage

(ODO)

If you want to stick to a 'water' metaphor you can use outflow:

• anything that flows out, such as liquid, money, ideas, etc

In many contexts, divergent is the best antonym for confluent.

Quoting the OED definitions:

Confluent, adj. […]

1a. Of streams or moving fluids: Flowing together so as to form one stream; uniting so as to form one body of fluid. […]

1b. Also said of roads, valleys, mountain-chains, etc., and fig. of trains of circumstances.

Divergent, adj. […]

1. Proceeding in different directions from each other or from a common point; departing more widely from each other; diverging.

(In your particular example, though, I agree with other answers that dispersal or diaspora is better than divergence.)