Android apps not working with HTTP proxy So I want to redirect my Android phone's HTTP traffic through a proxy running on my computer, in my case Burp Suite.  

I tried doing so by changing the WiFi settings and also by using the Drony app. I also installed Burp's SSL certificate on my phone.  

When I visit websites using Chrome, everything works fine both on HTTP and on HTTPS, and I can see all the requests on Burp. But when I use a different app - any app - I get a "cannot connect to the Internet" error message and I can't use the app.

Does anyone know how to fix this issue?  

I should also mention that my phone is not rooted.
Possibly you are trying to use apps over HTTP proxy which causes many apps to show connectivity error.
Try a VPN over proxy.
Connect as usual you connect to the internet through your HTTP proxy. AS chrome supports proxy, the internet works fine in it even with a proxy.
Then Search for Surfeasy VPN. 
I have tried many VPN's and only this and OpenVPN got success in establishing a connection with HTTP proxy. Try this, it works great. It even bypasses the restrictions over proxy if set up by Colleges, schools, Cafes.