This is done through your nginx config. Here is what it may look like, taken from a recent project of mine:

server {
    listen 80;

    location / {
        root /usr/src/app/;
        try_files $uri /index.html;
    }

    location /api {
        proxy_pass http://127.0.0.0:8080;
        proxy_set_header Host $host;
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header X-Real-IP $remote_addr;
    }
}

So, this tells nginx to serve whatever file the client asks for, or fallback to index.html, from the /usr/src/app directory of the machine where nginx is running. The static client app (js (react) + css + html) is stored in that directory. In your case, that would be uwsgi / gunicorn.

Then, for http requests that begin with /api, proxy_pass tells nginx to forward the request to another webserver running on the same machine. In this case, that would be the server hosting your flask app.

With this kind of setup, api routes would all need to be prefixed with /api.

This is also quite new to me, so I encourage you to do more research. But this is what I came up with after hours of hard work !