Proxying HTTP(s) traffic from Android devices through Burp should be actually no magic. Nevertheless you'll have to take some important steps into consideration:
Install Burps CA cert on the device
I usually access Burp directly and download the cert file (cacert.crt)
If Burp is listening on 192.168.1.1:8080, just go to
http://192.168.1.1:8080/cert to download the cert
Push this file to your device and install the certificate
Install ProxyDroid on Android
Set proxy setting globally or only for certain applications
In theory that's all! BUT: During recent mobile application pentest sessions, I've noticed that sometimes applications traffic is not being passed through the proxy, especially when the application does not connect to standard HTTP ports like 80 or 443. Besides that: What about SSDP and all other text-based protocols you would like to intercept in Burp? In most cases the proxy settings will simply be ignored and the traffic would be routed directly to the destination. In order to achieve my goal I'll be using iptables and some Burp settings most pentest aren't aware of. But first things first: The basics.