relating to 100 years : marking or beginning a century, with the example "the centurial years 1600 and 1700". But there is a word that is widely used to indicate the range of years or centuries covered by an article or book: history.
The flow rate increases 100-fold (one hundred-fold) Would be a more idiomatic way of saying this, however, the questioner asks specifically about the original phrasing. The above Ngram search would suggest that a one hundred has always been less frequently used in written language and as such should probably be avoided. Your other suggestion of by one hundred times is definitely better than a ...
In a scientific or mathematical context they might occur, in which case you should use standard index form 1×10¹⁰⁰ for one followed by 100 zeros. There is the joke word "googol" for this.
The title says it all. The original question goes like this: Fill in the blanks with the correct form of the given word. The flood which happened last week caused 100 people's _______ (death). I