luceos Ah yes, I was going to comment.
This is a strange one. There are no php issues since the install came up about the non-writeable directories - that was fine (I also went through each config ensuring they were correct.)
The strange part is the permissions were 100% fine and yet reported they were unwritable.
Not only does the owner of the files (flarum) have its own php process (which should of been enough by itself) but the nginx user (nginx) and flarum were both put into a group named webserver. Then all files were chowned (recursively) to flarum:webserver. and given permissions of 775 - which I confirmed by both owner:group and octal permissions, as well as checking more top-level directories (/var and /var/www)
The next logical step would be to simply su to each user that might be trying to access the directory and run touch /dir/foo and seeing if it succeeds. I would also ensure no caching is in effect..
I only had a short time and was a guest to the server, so I (very understandably) couldn't do much more then review and make suggestions. I've never had a permissions problem I couldn't solve so this is frustrating to say I don't know why it's not working..
It was also running CentOS.. I might start a discussion on what OS people are installing this on - cause I've noticed people having issues with CentOS here before..