How many Amperes to kill fruit flies and mosquitoes?
I am not an electrician and may not be the right person to answer this. But I recently read this paper (Keller et al., 2016) and maybe this helps ... Keller et al. (2016) have a look at laser induced mortality in mosquitoes. It might not be fully adaptable to your needs (there is not much context in your question, though; I have no idea what kind of trap you are trying to build ... if it's going to be a fancy laser trap, the cited paper will be your perfect guide through the building process - however, you have to figure out the automatic camera detection (they are planning that, too) for yourself as they have not published that, yet).

Now, giving a concrete answer: Keller et al., (2016) found that lasers with 0.5W to 4W are sufficient for efficient mosquito inactivation. If you are planning to use a plug bucket (230V) this would be (0.5W/230V=) 0.002A to (4W/230V=) 0.017A. You could also set this up with a 9V battery. With a 4W laser this would be (4W/9V=) 0.44A. Using a lithium-based battery this would last for about (1000mAh/(4W/9V=0.44A)=1Ah/0.44A=) 2.27h total laser time.

I do not know if this easily translates to electric current, though ...