I was flushing my radiator and I got water in my oil. What do I need to do?
The conservative thing would be to do an oil change.
But if it is a relatively small amount of water, I don't think I'd worry too much about it. Just drive the car soon so that the engine gets completely up to operating temperature and the water evaporates.
Where I would be concerned is if there was a chance that enough water got in so that the oil pump pickup could be sitting in a pool of water under the oil.
If you're concerned that a lot of water may have gone into the engine – for example if you mistook the oil fill for the radiator cap (I've done worse) – you can get a rough idea by looking at the dip stick. Oil will float on top of the water and if your oil is suddenly much higher then you know you've got a lot of water in there. Then I would change it for sure.