samtto as far as I know, Flarum only implements keyboard shortcuts for markdown formatting inside of the editor. No other actions on the forum have shortcuts. CTRL+ENTER is a browser shortcut to submit forms, so this usually works in most Flarum fields since native form elements are used almost everywhere even if submission ultimately happens via javascript.
However an extension could definitely map shortcuts to various buttons of the interface.
Since the "start discussion" and "reply" buttons are near the top, they might be reachable in a few TAB presses using keyboard navigation. But having header links or the side drawer open might cause a lot more tabbing required to reach them.