One doesn't eliminate the other.
Meteor is a full-stack framework which offers a collection of tools so that developers can use without any struggle and as @kayandrae said, React is a frontend library and Flux is an architecture pattern.
I don't know much about React nor Flux yet (gotta say Redux seems to be a better option) but you can use all of them with Meteor.
Meteor's future is to become closer to React and its ecosystem alongside with Blaze, the best decision (if you chose Meteor) would be Meteor + React.