No, there is no [z] sound in
اسبابکشی, have never heard anyone pronounce it like that, the [s] is pronounced like s in
ass, but shorter.
Except when someone wants to sound funny e.g. in a video, or speak in a funny way to his friends or significant other or kids/babies either to amuse them, or sound intimate and loving, then he might convert [s] sounds to
ش regardless of its location (and maybe convert some other sounds to something else as well, like
e.g. When you see/call your 2 or 3 years old niece, or your significant other, instead of asking her:
سلام، خوبی عزیز دلم؟
you might (and it's not uncommon nowadays) to ask her:
شلام، خوفی عژیژ دلم؟.
Note that even in informal (colloquial) language, this is not the proper way of speaking and it's only used is such specific cases (and even in these cases not all the time, but it's not uncommon either, these days).
And to learn to pronounce
اسبابکشی correctly, you can first try to pronounce each syllable separately like this:
as - bāb - ke - shi
Pronounce each syllable with a pause, and progressively try to shorten the pause, until you can pronounce it as one continuous word.