Well, I have a laptop which has good specs except its graphic card and I tried Kali Linux 2016.1 to dual-boot with it.
What should happen was : after installation (on a 100GB partition on my hard drive, which was a success), it should boot into GNU boot screen and let me choose whether I want to boot Windows or Linux.
What happened is : it booted normally to Windows even though Linux partitions was still there.
You had windows installed first? (I reread your earlier post where you said yes, and you didn't want to touch that. If you are worried about losing your stuff make sure you have backups). I don't use Kali, and I am not in current contact with the people that I know that do, but with most distros it will allow you to set up the partition like you described, and overwrites the MBR. I don't remember all the details right now, but the end result is that GRUB, or whatever, should give you the option to select what you want to boot after you complete installation and restart the computer (assuming GRUB knows where everything is).
I have a few things I would guess might be happening. Maybe GRUB isn't there, so it is still doing the windows stuff. I think you can have that give you the option to boot whatever you have on the disk, but it has been a while since the one or two times I went that route. Another possibility is that Windows is the default, and GRUB is booting it before you notice it (or automatically...it can do that, right?).
I haven't ever encountered the third thing I have in mind, but I have seen it discussed since it seems to be the direction predatory companies are taking the PC market. Out of curiosity, how old is this computer, and does it use UEFI? If yes, have you looked at the settings? I don't really know what to look for, I only suspect that there is a tiny possibility that something may be preventing you from messing with the MBR, either because someone assumes you are too stupid to know what you are doing, or because Microsoft made a deal with them and wants to make sure you stick with Windows.
Lemme look at a few things and I might be back with more.
Edit: I am still trying to read up on UEFI and GPT and such, however I have a nagging thought. Feel free to disregard this. I usually recommend people not use Kali as their main distro. It is probably fine for general use, but it is really designed for a specific set of purposes. Honestly, I only ever used it and Backtrack as liveCD/DVD/USB, and never installed it. Installing it for everyday use makes me think of script kiddies. (Edit edit: I just saw your location...) All of the tools it comes with can be installed on probably any distro.
[doublepost=1464439595,1464437318][/doublepost]Possibly of interest:
https://en.wikipedia.org/wiki/Unified_Extensible_Firmware_Interface#Secure_boot_criticism