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.
KEEN-Oh-Poe-DEE-Um ?
I think that’s the way I’ve most often heard it.
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.
So, you’re telling that English speakers pronounce chlamydia with “k” and not “h”?
Yes. “Klam”
Given how some well known public figures pronounce China, I’m surprised nobody has suggested proununcing it as:
However, I think the approach of pronouncing it based on naming origin makes sense.
Being German, I’m going with the pronunciation example posted here.
Well, it means goosefoot, named after the goose genus Chen (as in Chen caerulescens, the snow goose).
Chen with the Ch like kennel or charcoal?
Ha, I thought that example would come up. I admit I’d say it Chen and not Ken.
On the rare times when I say it, I pronounce it “chen” also.
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.
Is your pronunciation of the ‘th’ in Lith as in the the or think ? 
Rhymes with pith.
(The gentleman you asked in your message is, sadly, no longer with us.)