Yes, this kind of thing is possible.
There is no limit to how many genitives you can chain.
If you want to describe the properties "of the food of a dog of a man of a city of an empire", you can translate it as cibi canis viri urbis imperii.
Of course this gets silly at some point, but grammar does not limit it.
"Of the victories of Rome" is an excellent translation of victoriarum Romae.
But broader context will determine what the best translation is.
If Romae is singular dative or plural nominative instead, then you need to translate it correspondingly.
Latin tends to use adjectives for things like this, so I would translate "of the victories of Rome" from English to Latin as victoriarum Romanarum ("of the Roman victories").
But the genitive is grammatical as well.