You could try SandroProxy, a free app developed by XDA Developers member SandroBSupp.
It can act as pass-through proxy, traffic is not stored, ssl tunnel
remains the same to server.
SandroProxy doesn’t require root. All you need to do is to hit the
Play button and the app will serve as an SSL MITM proxy (Secure Socket
Layer Man-In- the -Middle-proxy). Your HTTP/HTTPS requests will be
redirected through a web server, making your sent and received data
invisible and, thus, protected.
You can access transparent proxy, a network layer proxy which, in turn, redirects the traffic needed by your phone for proxy identification. The only traffic that this proxy modifies are those which are absolutely necessary for proxy identification and authorization.
Uses proxy on localhost:8008
Haven't used it but it looks promising for what you're trying to achieve.