How much of the "Programming Elixir" book must I go through before I can start learning Phoenix?

Try not to “go though books”.

Learn the basics of the language:

• conditional statements, looping, functions, maps and lists
• Then find the documentation for the standard library

Notice I did not say to “learn” the standard library.

Then, assuming you have a real project (you do have a real project, right??), start building it with Phoenix.

As you build it, you will learn.

Trying to read a book on Elixir or Phoenix without building something as you learn, will get you exactly nowhere.