When they fly, there's no current. They just have potential compared to ground. Also presumably their electrical charge is very low and there's going to be hardly any amps when they discharge.

In the same vein, if your carpet gives you a static shock, that's likely going to be thousands of volts. But obviously there isn't actually a lot of energy stored (all you did was convert some friction), so there's next to no amperes, little work the electricity can do, and thus no harm.