Is it possible to diagnose gynecomastia with a chest x-ray?

Not Necessary. In-person consultation with your family practitioner and/or plastic surgeon is a good place to start. Accurate history and physical examination is important. Eliminating “causes” of gynecomastia is also important. Surgical treatment usually involves partial excision of the glandular tissue plus/minus liposuction surgery. Again, much of what is recommended will depend on specific physical exam.
Don't need. You do not need chest x ray to diagnose gynecomastia , simple clinical examination is suffice.
Yes but... That would be like diagnosing a train going by with a seismograph . The diagnosis is readily made by physical exam. Whereas an MRI could give information about what percentages of the male breast is composed of glandular tissue, this test is unnecessary to plan surgical management which is best done by utilizing slim lipo unless there is a distinct mass in which case you need mammogram/mri.
No. The diagnosis of gynecomastia is a clinical one. If you are a male and you appear to have breasts, you have gynecomastia. It may be all fat because you're middle-aged or overweight (pseudogynecomastia) or you could truly have breast tissue.