Yes, it's perfectly fine for her to have a chest x-ray. She should let the radiographer know of any medical issues, but an x-ray is not going to be harmful if she's breastfeeding.
I remember the times when I just became a mother, I was so worried about everything. However, I personally have done x-ray exams pretty often when I was breastfeeding. It was totally alright, not considering the fact that my milk was over when my baby boy was 4 months, I was pretty upset, however my husband said that I shouldn't be bothered that much, because mother-nature knows better, so probably it was high time for ordering special formulas from anyorganics.com. Really grateful that I had managed to discover this online shop before I went to our local shops where such formulas cost three times more expensive.