In your examples, we say:
Je m’en fiche, je m’en vais,…
The word “en” is a pronoun for the complement of the phrase.

In all the examples you listed, "en" is the pronoun serving as the COI.

Example:
Sa voiture? Elle s’en fiche. (her car? She doesn’t care about it.)
"en" = "sa voiture" (her car) is the COI.

You could have said: Elle se fiche de sa voiture.

So because "en" is the COI, it’s incorrect to say "je m’en (verbe) de COI". Still it’s used all the time, for example: Elle s’en fiche de sa voiture. In that case "en" still means "sa voiture". You can think of it as adding a precision after you’ve stated the main sentence with the pronoun: Elle s’en fiche. (de sa voiture)

J’en m’en (verbe) is never correct, and never used.