"There are three colors on the German flag."
Translation:Alman bayrağında üç renk var.
Yes, such things are compounds of a noun referring to the inhabitant.
Compare "Türk kahvesi", where it's a bit clearer since the adjective and the noun are different in English -- we say "Turkish coffee" in English, but Turks say literally something like "Turk coffee", i.e. the coffee of Turkish people.
Similarly here, the German flag (with "German" an adjective), in Turkish, becomes the German flag (with "German" a noun), the flag of Germans.
Similarly with "Spaniard food, Frenchman hymn" etc. where we would say "Spanish food, French hymn".
They aren't "suggestions", they're "hints" to help you remember.
Also, the hints are associated with a word (in a given spelling) and will be shown in every sentence that has a word with that spelling, whether that hint is appropriate in that sentence or not.
Compare English "like", which can mean "think something is good" (I like chocolate) or "similar to" (It tastes sweet, like chocolate) -- in a sentence such as "We like tea", it would still show the hint "similar to" even though it would be completely inappropriate there.
That said, though, http://tureng.com/en/turkish-english/flama says that flama is a "pennant; streamer; flag", so it's not completely wrong.
Perhaps it's not used for the flag of a country.