Proficiency in Rust isn't required to get started. It helps, but I think you'll be able to build a usable webapp using only this guide. For business logic beyond the GUI, more study may be required. The official Rust Book is a good place to start. Especially-relevant chapters are
Using Structs, and
Enums and Pattern Matching.
You should be able to get by with just the basic Rust syntax common to most programming languages, eg conditionals, equalities, iteration, collections - and how Rust's borrow system applies to strings. A skim through the first few chapters of the Book, and the examples here should provide what you need. Rust's advanced and specialized features like lifetimes, generics, smartpointers, and traits aren't required to build an interactive GUI. If you run into a syntax or borrowing/ownership problem, the compiler will often recommend a fix.
Experience building websites using HTML/CSS or other frameworks is required. Neither this guide nor the API docs describes how web pages are structured, or what various DOM elements, attributes, styles etc do. You'll need to know these before getting started. Seed provides tools to assemble and manipulate these fundamentals. Mozilla's MDN web docs is a good place to learn about them.
The design principles Seed uses are similar to those used by React and Elm. If you're familiar with how to set up interactive web pages using these tools, you'll likely have an easy time learning this.