That study might be the best available, but it isn't very convincing - they are analysing a large number of countries and it doesn't look like they gathered the data first hand.
Are all the statistics using a consistent definition of human trafficking? I have no faith that data between different countries is comparable on this issue, especially when it was apparently gathered from other sources. That is the sort of approach that gets Sweden called a 'rape capital' [0].
It is an extreme claim that legalising something causes crime rates to increase. They advance a plausible idea for the mechanism, but it seems reasonable that they are picking up ghosts in the data rather than a real effect. Correlation and causation issues might also be at play somewhere, and the scope of the study is just too big to pick it up. If there is a secondary source on one country that talks about a before-and-after observed change that might be interesting.
Basically, I'm not dismissing it out of hand, but it seems pretty reasonable that legalising drugs/prostitution/whatever automatically reduces crime and this study doesn't meet a reasonable bar of evidence. Maybe if it were combined with a good single-country study that highlighted the mechanism a bit more - but the uncertainties in the case study are enormous. The numbers cited in the report for Germany, for example, could be optimistically (optimistic to the point I feel disingenuous, but I don't think I'm saying anything statistically outrageous) spun to say that it is human trafficking may have declined from 19,740 (1996) to 12,350 (2003) with the legalising of prostitution +.
[0] https://www.thelocal.se/20170221/why-sweden-is-not-the-rape-...
+ Footnote 38 notes that Germany changed their definition of human trafficking victims between 1996 an 2003 to include more people, although they don't think this accounted for the majority of the increase.