I have formatted your output as code, so it's a little easier to read:
root@no:/var/www/html/forums/vendor/xengine/flarum-ext-signature/js/forum/src/Components# composer require flagrow/byobu
No composer.json in current directory, do you want to use the one at /var/www/html/forums/vendor/xengine/flarum-ext-signature? [Y,n]?
Do not run Composer as root/super user! See https://getcomposer.org/root for details
Using version ^0.1.2 for flagrow/byobu
./composer.json has been updated
Loading composer repositories with package information
Updating dependencies (including require-dev)
Your requirements could not be resolved to an installable set of packages.
Problem 1
- Installation request for flagrow/byobu ^0.1.2 -> satisfiable by flagrow/byobu[0.1.2].
- flagrow/byobu 0.1.2 requires flarum/flarum-ext-markdown ^0.1.0-beta.5 -> satisfiable by flarum/flarum-ext-markdown[0.1.x-dev, v0.1.0-beta.5] but these conflict with your requirements or minimum-stability.
Installation failed, reverting ./composer.json to its original content.
You get an error: No composer.json in current directory. The reason: You are not in your flarum directory which seems to be /var/www/html/forums. To verify for the right directory, make sure that there is a file named composer.json in it.