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 ...
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Add Yahoo as a preferred source to see more of our stories on Google. Variety has released its list of the 100 best comedies of all time, ranked by editors and critics. The films go back more than a ...
Variety Reveals Top 100 Comedies of All Time: See the top 10!
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:
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.