It is not a security question. It depends of how to configure your vm networking. Is a bridged machine? is a NAT vm? is host-only?
Host-only: you can't access to the host network from the vm... as name says, you can reach only the host, and not its network.
Bridged: If vm is bridged it will be another "independent" machine on your network, so you already are on the same network as your host machine is.
NAT: You can access to your host's network through host.
I guess you have a DHCP in your host's network, so setting vm as bridged is the easiest solution I think because you must do "nothing". If you have DHCP on your host's network, your vm is going to get an automatic IP and that's all. You can reach the same as your host machine. So you can set up Burp on your Kali vm and configure your browser (inside Kali vm too) to use the Burp's proxy (usually http://127.0.0.1 on port 8080 by default). Don't forget to install Burp's certificate to reach https pages. To do this is easy, enter with your browser (inside Kali vm too) to the page http://127.0.0.1:8080 , download the certificate and import it to your browser as truted authority, as simple as that.
Not sure what you are doing wrong, is not complicated. Can't help more without more data.