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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 ...
As you note, "percent" means "for every hundred," so there is nothing at all wrong with percent values greater than 100 when discussing proportions, e.g. profits increased by 120%. Like fractions, however, percent values are longer to express than multiples, so for values much greater than 100 you may hear them less frequently:
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.
Because killing 99.99% of germs is very, very different from killing all of them. In any given population, there are many, many, many germs. And leaving one alive is (theoretically) sufficient for it to reproduce. So if you're not killing all (100%) of them, there's still a chance you'll get sick.
37 Wikipedia lists large scale numbers here. As only the 10 x with x being a multiple of 3 get their own names, you read 100,000,000,000,000,000,000 as 100 * 10 18, so this is 100 quintillion in American and British English and 100 trillion in most (non-English speaking) other places.