Both are okay. The first meaning, let me give you an example: 我翻来覆去睡不着。（wǒ fān lái fù qù shuì bu zháo）I tossed and turned and couldn't sleep. And the second meaning, 他翻来覆去地讲这个故事。（tā fān lái fù qù de jiǎnɡ zhè ɡe ɡùshi）He told the story over and over again. By the way, I have updated some videos for Chinese learners. If you want to learn more idioms, you can check out this link:https://www.instagram.com/easymandarinwithmandy/guide/easy-chinese-idioms/18018162811678462/?utm_campaign=&utm_medium=&utm_source=ig_web_copy_link

Thank you. And how should I understand the characters on their own? Are 翻 and 覆 the word 翻覆 separated or are they independent characters? What would be the literal translation?

Both are fine. Mostly it means over and over again.