There is a little bit of discussion about this issue here:
You would either have to build the qubes-template-kali-core or increase Dom0’s partition size.
I have made a little size comparision between kali-core (~4.5 GiB) and different other template flavours in November of last year:
If you should not be operating under very strict internet access conditions, I can really recommend kali-core as DispVM and just apt-get whatever you need in that specific situation.
As soon as you are using a more enriched template flavor, there is a lot of stuff included that you probably never need.
Additionally kali-core should be a little bit more stable on Qubes and accelerates the updating process significantly.