Several human studies and some animals ones. Keep in mind that most of the human patients had severe liver disease and as such their ammonia levels were quite high (some people were in coma). As such, the high doses of zinc used in those studies (150mg-200mg elemental zinc per day) are probably only needed in such extreme cases. Amazingly, zinc was able to reverse encephalopathy caused by high ammonia levels in quite a few patients.
For most people without such severe liver conditions, much lower doses of zinc should be able to reduce ammonia. I'd venture a guess that 50mg of elemental zinc is probably enough but feel free to experiment to find out what works best for you.
http://www.ncbi.nlm.nih.gov/pubmed/25280421
http://www.ncbi.nlm.nih.gov/pubmed/20822500
http://www.ncbi.nlm.nih.gov/pubmed/8621138
http://www.ncbi.nlm.nih.gov/pubmed/1505922
http://www.ncbi.nlm.nih.gov/pubmed/2626852
http://www.ncbi.nlm.nih.gov/pubmed/3218283
http://www.ncbi.nlm.nih.gov/pubmed/6147551
http://www.ncbi.nlm.nih.gov/pubmed/546221
For most people without such severe liver conditions, much lower doses of zinc should be able to reduce ammonia. I'd venture a guess that 50mg of elemental zinc is probably enough but feel free to experiment to find out what works best for you.
http://www.ncbi.nlm.nih.gov/pubmed/25280421
http://www.ncbi.nlm.nih.gov/pubmed/20822500
http://www.ncbi.nlm.nih.gov/pubmed/8621138
http://www.ncbi.nlm.nih.gov/pubmed/1505922
http://www.ncbi.nlm.nih.gov/pubmed/2626852
http://www.ncbi.nlm.nih.gov/pubmed/3218283
http://www.ncbi.nlm.nih.gov/pubmed/6147551
http://www.ncbi.nlm.nih.gov/pubmed/546221