Tractor Supply and most feed stores such as Rural King, Southern States, and others  would sell 35 ml syringes and 18, 20, and 22 gauge needles. They are usually locked up, and some state my have a state law not to sell them.
Every case is different, but my only hen that I chose to drain, lived only about 2 weeks. I had hens with symptoms of water belly who lived a longer time. The risks are introducing infection and death. Once the needle is inserted and then removed, the site can continue and drip for hours. I would give some electrolytes in water or Poultry NutriDrench 2-3 ml orally after draining.