Flux is a way to organize interactions with data and business logic, so that React only has to worry about the UI. Specifically, it breaks down behaviours into functional streams that don't interrupt each otherr.
AFAIK (I have not worked with Relay yet) Relay is a data layer, (which currently flux handles already). Relay is component based, as opposed to flux, which handles data in a top-down manner.
As I understand it, when we implement Relay, flux will be relegated to handling UI behaviour and changes. So, React would handle DOM manipulation and rendering, Flux will handle user behaviour and changes to state, and Relay will provide the data.