Flying birds are a whole topic itself. FAST moving birds require specialized gear (to track and focus), and very importantly technique. Slow moving birds or stationary birds are much easier to deal with. The longer the lens, the $$$$ it will be. Long zooms, start with the Sigma 150-600 at about $1,000, and go up $$$$. For flying birds, you want a body with good zone autofocus. That means upgrading from your D3200. I would go with the D7500. At the top of the stack is the D500, for fast moving birds.