I think incest would increase because I think more people would at least try it. Like any other sexual encounter people should practice safe sex to prevent unwanted pregnancies and STDs. I personally wouldn't have a problem with it, As long as it is between adults and its consensual. I would try it!
As much as I hate the idea and find incest to be completely immoral and down-right disgusting, I feel it is a matter of common knowledge that if it were to be legalized one day, it would only increase cases. There are a lot of people out there who believe in incest, so if it becomes legalized they will then be aware they are not committing a crime.
Yes, legalizing adult incest would increase it. Whenever something is illegal, law-abiding people will avoid it. Making something illegal will not completely stop something from happening, but it will happen less. Conversely, making something legal means it will happen more. Some people will still avoid it, but incest rates will go up, because people will think it is now something they have the option to choose from. When it becomes a legal choice, more people will do it.