The particular points you asked about are almost correct: von denen is pretty much the best choice except for being plural, wird belongs at the end of the dependent sentence, and "Kilo" is in accusative, not genitive.
However, there are other errors and a bit of ambiguity. First, the source phrase doesn't have a verb, so adding one in the German translation is inappropriate without knowing the context. (It seems you didn't post the entire source, because there's no mention of the UK there either.)
I'll assume the source is "In the UK, there's 23.5 billion kilograms of household-waste ..." since that fits the translation best.
The translation is
Im Vereinigten Königreich gibt es jedes Jahr 23,5 Milliarden Kilo Hausmüll, von dem 9,4 Milliarden recycelt wird.
- No comma after "Im Vereinigten Königreich".
- Gibts or rather gibt's is a colloquial contraction and inappropriate for formal writing.
- Milliarden needs to be plural.
- Kilo is not put into plural because it doesn't stand alone but rather modifies Hausmüll, which is uncountable.
- Since it is uncountable, the appropriate form to use in the dependent sentence is singular. Although plural (von denen combined with werden at the end) would not raise many eyebrows, singular is more correct.
More idiomatically, though, you wouldn't write gibt es at all; instead you would probably write "Das Vereinigte Königreich produziert jedes Jahr ...".