Burp Suite is not available for iPhone but there are a few alternatives with similar functionality. The best iPhone alternative is HTTP Toolkit, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 25 alternatives to Burp Suite and four of them are available for iPhone so hopefully you can find a suitable replacement. Other interesting iPhone alternatives to Burp Suite are Charles, Proxyman and Proxygen.
HTTP Toolkit is a beautiful, cross-platform & open-source HTTP(S) debugging proxy, analyzer & client, with built-in support for modern tools and automatic interception for clients from Docker to Android to iOS.
Spain
EU
Charles is an HTTP proxy / HTTP monitor / Reverse Proxy that enables a developer to view all of the HTTP and SSL / HTTPS traffic between their machine and the Internet. This includes requests, responses and the HTTP headers (which contain the cookies and caching information).
New Zealand
Monitor, intercept and debug HTTP/HTTPS and WebSocket traffic on macOS, iOS, Windows, and Linux. Includes advanced features such as Breakpoint, Map Local/Remote, scripting, filtering, reverse proxy, DNS spoofing, and automation for backend development.
United States
Proxygen is the best HTTP proxy tool for testing apps and debugging remote API endpoints right on your iPhone, iPad and Mac. And it’s built to delight you while doing it.
FinlandEU
