Will brake fluid damage power steering

Whew! I read that wrong the first time. Flushing the power steering system should be sufficient.

Putting any hint of petroleum product in the brake fluid is a major disaster. That includes engine oil, transmission fluid, and power steering fluid. That will destroy the rubber parts in the brake hydraulic system. The only proper fix for that is to replace all parts that have rubber that contacts the brake fluid, and flush and dry all the steel lines.