I always assumed the CH was pronounced as K for names derived from Greek (unless it’s Latin). As in the word chelate. I pronounce the turtle genus Chelydra with a K sound although I’ve heard some pronounce it with a CH sound. And I’ve always heard Chenopodium pronounced with a K sound but then I’ve not heard it said that often.
In the case of chinense I’d pronounce it with a CH sound since it is derived from the name China.
Added: Even if you’re not sure of the origin of the scientific name, I almost always pronounce the CH as a K as it usually is pronounced in most scientific terms: chemistry, chordate, notochord, chelate, Chlamydia, etc.
Absolutely, CH was used for the Greek Χ, not for the Greek Κ.
And it was used for neo-latin so there is much better case for the velar fricative rather than the aspirated K from classical Greek, but I do admit there is some case for those who would go for the aspirated K as in the English word “cat”. Definitely not the normal K as in the English “dark”.
And most definitely not the [t͡ʃ] sound as in the English word China. Although I can see why one would want to pronounce it that way for chinensis. But only there please.