Twitter app on iOS 9 doesn't connect through proxy
iOS 9 implements App Transport Security on each individual application. This is a setting that is enabled by default on all iOS 9 apps. Application developers that wish to allow their apps to be proxied can disable this setting in the applications plist file. If you are on a jailbroken device you can also manually modify this file.

Alternatively I found this that should work, haven't tried yet though
https://nabla-c0d3.github.io/blog/2015/12/01/burp-ios9-ats/