What would happen if one plugged a USB flash drive into a phone charger?

Absolutely nothing bad would happen if any standard USB device were plugged into a USB charger.

At worst any "power" LEDs that light up when plugged into a computer would still light up, but nothing more.

A USB charger puts out 5V unless the device negotiates a higher voltage. That means a standard 5V USB device would power up.

There wouldn't be any "host" USB controller, so the stick would just sit there waiting to be asked what it is and getting no communication. It will not magically become a powered wifi hotspot or a powerline memory stick, nor will either burst into flames.

It would take a small amount of power and that is all.

That's it.

If it is a "standard" phone charger (5 Volts), nothing should happen to it. But it will not do anything either. So you should be fine.

A wireless adapter may do nothing, or it may (if a cell adapter) start to work. I do that with my HUAWEI stick.