The sentence means: When flies fly behind flies, flies fly after flies.
The word order in German is a bit different so for comprehension, here's what the individual words mean: The "Fliegen" that starts with a capital letter is the plural of "Fliege" which is the animal "fly". The lower case "fliegen" is the verb "to fly". hinter = behind hinterher = after
Simply 'muŝ'. Muŝa, muŝi, muŝe, ktp...
To find a root, take off all prefixes and suffixes you see. In this case, the only thing you had to take off was the noun suffix, -o. In other cases, it may be the prefix ge-, or suffix -et-, or conjugation -as, etc. so the root of 'flugas' would be 'flug'! :) hope this helps.
Then, what does the verb muŝi mean? Does muŝo muŝas make sense in Esperanto?
Vortaro.net tells me that there is no muŝi yet.
As to flies, I am recalled with an idiom in my mother tongue ying-ying-gou-gou dated ~2500 years ago, a metaphor with flies and dogs referring to dirty things; the first ying means fly, the second means dog, while the second ones are homophonic verbs.
Muŝi can be translated into English as "to be a fly". In the same vein as boni: "to be good".
muŝo muŝas = a fly is a fly (or, we could say "a fly flies"... but flies = muŝas, not flugas, or even muŝoj)
If a word is made into a verb that isn't normally a verb, it can get a little wonky and need a couple of additional words when translating. But that doesn't mean it's wrong!
This is how you make sentences in Esperanto that is hell to translate. :)
蝇营狗苟! I distinctly remember my Chinese teacher talking about that... Haha :D