How to keep a flask submerged in water?
The vinyl coated lead rings suggested in the comment are a great solution. They are, however, expensive and take time to order. There is also the cost of shipping.

A quick and less expensive route is to use a PVC flange and attach what ever heavy metal you have (steel, cast iron, lead fishing weights). Epoxy to flange or drill holes and tie. You may want to paint the metal to avoid rust or other reactions with the metal.  

Home Depot has inexpensive 3" flange or 4" flange.