@rvasilev
I was able to install Flarum on Heroku, however, I recall Heroku resetting all files after X minutes, and because Flarum modified local files, some things broke.
I do not remember if I actually managed to put it working or not, so sorry about that.
rvasilev The directory is not writable.
Please chmod this directory and its contents to 0775.
You need to change the file's permissions to 0775, which you can find how searching 'chmod' on this forum.
Execute the following in the forum's folder, it may work for you (from Kulga )
chmod -R 0775 forum
You may need to change the group to www-data
or something else as well:
chgrp www-data .
chgrp -R www-data assets/ storage/
Hope that helps ?