I suggest autoclaving your flasks. Add a little bit of distilled water to help generate steam for the inside. Go ahead and sterilize dry your glassware in the autoclave for some 30 min at 130 C. By the way, this can be done provided your glassware is pyrex quality. Good luck!
I do not know your application and use of these flasks. However for low level ammonia/ammonium analysis based on indophenol blue method I have experienced and recommend to use dedicated glassware. For rinsing, let the flasks stand overnight with addition of indophenol blue reagent and then flush 3x with deionised water before use. You will see the development of blue colour if ammonium is present. Rinse after use with deionised water and keep glassware stored filled with addition of indophenol blue reagent and caps on until next use.
Thank you for the suggestions! After trying these, I was still having ammonia contamination and will now be using plastic flasks and sampling tubes instead.