How safe is it to have a gold crown sitting next to an amalgam filling?

Very safe! As a dentist with over 25 years of experience, i'd venture to say millions of gold crowns are sitting there next to amalgam fillings. The vast majority of them (probably 99% or more) exhibit no interaction (significant galvanic current) causing symptoms. There is disagreement among dentists on this topic. Some dentists are very anti-amalgam and very passionate about it. Me? I place amalgams!
Safe, but.... I have seen galvanism in the mouth, exactly as you describe. It is rare. As amalgam use decreases this will be even less of an issue. One more benefit of adhesive dentistry that is metal free.
It is Safe. There is no special concern to have gold next to amalgam. You may be asking this because in chemistry, you learn that two different metals touching like this with an electrolyte (saliva) will produce an electric shock. While this is possible chemically, this effect is not noticed because the electrons are fully discharged when the restoration is placed. So if there is a shock, you are still numb.
Safe. A gold filling next to a silver amalgam filling is totally safe. Don't worry, as NIH and the CDC have deemed these restorations as safe for all age groups and have decades of scientific evidence to back up these claims.
Gold and amalgam . If gold and amalgam fillings are right next to each other in your mouth, an electric current can result from interactions between the metals and your saliva, resulting in discomfort. This is called "galvanic shock." Replace amalgam filling with porcelain, composite or gold. Hope it helps.
Not very safe.... Gold is an excellent restorative material. Amalgam is a bad restorative material. Galvanic interaction does occur and causes greater mercury vapor release from amalgam fillings. Mercury vapor is hazardous to your health. Read about mercury free and mercury safe dentistry and realize that your amalgam fillings should be replaced. Several countries ban amalgam !