Could bilateral chronic pain (3-4 mos) in back near ribs that gets worse with deep breathing, movement, and pressing on area be from kidneys?

Sure can. Worth a visit to your doctor. And drink lots of fluids in the mean time.
Most likely not. The area you described , the duration, the aaggravating factors point either to musculoskeletal origin. However , this is not a gurantee or substitute to through evlauation by you doc.
NO. Unlikely to be kidney stones on both sides with the symptoms you describe.