Welcome! With a high quality USB charger, you should be fine. (Edit: I'm assuming that information from elsewhere tells you that 1A is enough current. Edit: 1.2A is stated in
the manual.)
Of course, if it doesn't just work, switch off immediately. It's possible that there will be some component failures - but that's an adventure for another day.
Edit: for some modern computers, the 5V from a charger won't be enough, mostly due to voltage drop on the wires, but I think the KIM-1 won't be so picky. And there's no harm if you find you've under-volted it and it doesn't work well.