Okay turns out it has to be named just fi.mo if it’s in the themes languages directory.
I solved my issue but it’s not how I expected. My WP is in Finnish so I created flat-responsive-fi.mo with the translations and placed that in wp-content/themes/flat-responsive/languages but it’s not picked up from there. Then I moved it to wp-content/languages/themes/flat-responsive-fi.mo and now it’s picked up.
Is that how it’s supposed to work? I thought following line in functions.php made it pickup the translation from the themes languages directory.
load_theme_textdomain( ‘flat-responsive’, get_template_directory() . ‘/languages’ );