I'm trying to run multiple instances of OSBOT in Mirror Mode, each time however it hooks itself onto the same OSRS client, is there a way to select or force the Bot to hook onto a client window of my choice?

I'm using Proxifier to open clients in different windows you see

Not afaik. I think it's random. I've also had 2/3 clients hook onto the same vanilla osrs client before. 

use virtual vms

Like Chris mentioned, the most reliable way is to launch virtual VMs to where you contain 1 bot to 1 client. Otherwise if you have multiple copies of the client open the order in which it attaches seems to be random.