だしを作るためのかつお節を使う量 is "how much [European people] consume katsuobushi for making dashi." So this 量 refers to the amount of かつお節.
Consider the following "original" Japanese sentence:
ヨーロッパの人々はだしを作るためのかつお節を {たくさん|100グラム} 使う。
European people consume {a lot of | 100 g of} katsuobushi for making dashi.
Note that the amount is expressed adverbially as usual in Japanese. だしを作るための modifies かつお節, not 量. Let's omit the obvious subject:
だしを作るためのかつお節を {たくさん|100グラム} 使う。
Replace the bold part with 量 and pull it out to the end to form a relative clause:
だしを作るためのかつお節を使う量 …①
You can express the same thing using the passive voice. Starting from this sentence:
(ヨーロッパでは、)だしを作るためのかつお節がたくさん使われる。
(In Europe,) a lot of katsuobushi for making dashi is consumed.
By pulling out the たくさん part, you get this noun phrase:
だしを作るためのかつお節が使われる量 …②
how much katsuobushi for making dashi is consumed
The noun phrases ① and ② say the same thing. The only difference is that ① is active and ② is passive.
Here are some similar examples of "adverbial-head" relative clauses:
- 13時に昼食を食べた。 I ate lunch at 13.
→ 昼食を食べた時間 the time when I ate lunch
- 東京でその映画を見た。 I watched the movie in Tokyo.
→ その映画を見た場所 the place where I watched the movie
Obviously you don't eat 時間.
Lastly, in this example, you can change だしを作るための (modifying the following noun) to だしを作るために (modifying the following verb) without altering the meaning of the sentence.