You don't need Flux/Redux to use React. React without a Flux-alike is very much like Sinatra compared to Rails. If your goal is to learn React, Flux gets in the way, and you shouldn't bother.
Browserify/Webpack is a giant pain and my least favorite part of this programming environment, but I'm not clear what it has to do with React. Is the concern here that React is packaged in such a way that you can't use it with a simple script inclusion, and that you must use a bundling system?
Router libraries are even less essential to React than Flux. I've never used one.
Webpack is used for hot reloading otherwise Gulp can suffice to provide you with a command to compress your css and jsx files. You could do it manually with the cli to begin with but I'd use a build automation tool going forward.
Browserify/Webpack is a giant pain and my least favorite part of this programming environment, but I'm not clear what it has to do with React. Is the concern here that React is packaged in such a way that you can't use it with a simple script inclusion, and that you must use a bundling system?
Router libraries are even less essential to React than Flux. I've never used one.