I'm not an egoist anarchist, but the other answer to your question is wrong and I don't want it to be standing there without correction. Egoism in an anarchist context goes back to "The Ego and His own" by Max Stirner, a German philosopher. He was not an anarchist, but has been and is still very influential on the movement.

Here's his works on the anarchist library: https://theanarchistlibrary.org/category/author/max-stirner

I haven't read it myself yet, but read some short summaries. Afaik he wants everyone to acknowledge that we're basically working in our own self-interest all of the time BUT that this requires cooperation and that helping others without immediate material benefit can be part of our self-interest, e.g. because it makes us feel good or because it builds relationships that might be beneficial later.