The problem is that you're installing kali linux. Don't do that, it's meant to be used as a live environment. If you want to install a linux distribution that has access to kali's built in software install ubuntu or debian.
As for why the installation is failing, it could be for a variety of reasons - posting the exact steps you went through to get here and your system configuration might help us determine which one it is. For instance, are you *sure* you have enough disk space and that you selected the correct drive in the installer? How did you partition said drive?