Brake fluid added to the coolant reservoir

Here is a guide that will help with this in case you need it:

https://www.2carpros.com/articles/coolant-flush-and-refill-all-cars

To answer your question on this, it is unlikely that it did major damage. The main thing you would need to worry about is the heater core plugging.

What I would do is flush the cooling system like you are planning and then use a laser temp meter to check the temperature on both lines coming from and going to the heater core. They should be about the same.

https://www.2carpros.com/articles/how-to-use-an-infrared-temperature-meter

If that is okay then I would not worry too much about it as it is not uncommon to have oil and other contamination in the cooling system. It is pretty resilient, even though brake fluid is more corrosive.

Let us know if you have other questions. Thanks