Is it normal that the amalgum in my filling is turning black?

Yes: The amalgam(silver, mercury plus other metals) will tarnish. The will appear darker grey to black depending on what metal combo, mouth enviroment, to diet. This tarnishing helps them to reseal themselves to last longer. It makes the teeth look darker and stains them or the gums.

Definitely, yes: An amalgam filling contains a mixture of metals such as tin, copper, silver and mercury. They do tend to turn black over a period of time which can look unattractive.