If the both originate from Proto-Sino-Caucasian, then Chechen language should be close to Chinese. Is there any indication for this?
The answer is no. For two reasons:
Just because a language might belong to the same family as another language, they may not be outwardly similar at all. Just compare German, Russian and Persian. It takes a very close historical study to link them. Or even just German and French.
Many of these proto-X families are extremely hypothetical and the evidence for them is tenuous and controversial based on a vague similarity of a few words, a few sound parallelisms and some proposed historical connection. Not infrequently being the pet theory of one author. Of these, Proto-Sino-Caucasian is one of the less widely accepted.
I am Chechen and I speak Chinese as well. There are some words in both languages mutually understandable and spelled the same way - I guess that's ONE thing that (if it could) would made Chechen close to the Chinese.
The other thing is the tones, both in Chechen and Chinese.
I dunno how what methods the linguists use to refer one language to the other. I have noticed they (those who do so) do not even have a proper knowledge of Chinese/CHECHEN to be able to COMPARE them.