So far as I know it’s not a common procedure so I wouldn’t be surprised if most ER doctors were unqualified. Gout is also a chronic condition and so not something an ER is supposed to deal with if it can be avoided.
I’m sure they would rather give you pills and get you out of the ER quickly. Have you exhausted the common pharmaceutical options by the way?
Can your rheumatologist’s office recommend another specialist?
Anyone who does joint fluid aspiration ought to be able to give you an injection as well. Maybe your rheumatologist does that themselves. But mine would rather refer you to a skilled hand who is setup to handle emergencies.