Yeah, shipping from US to Europe is not cheap these days. The USPS rate you got is probably going to be your lowest, but I am subscribing to this thread to see if someone offers a cheaper alternative.
Whenever I buy something for someone in Europe these days, I try to buy it on Amazon DE or UK because the shipping is cheaper that way.
Did you ask them if they have a surface mail option? I believe flat rate still goes by plane over the ocean. Surface mail like used for batteries should be cheaper. Will take a extra couple weeks or so to get there