The Burst compiler is closed source. However, if you import the Burst package [1] into your Unity project, you can see most of the source using ILSpy [2].
In your project, see the directory: "Library/PackageCache/com.unity.burst@<package-version-here>/.Runtime". The DLLs you'll want to inspect are: "Burst.Backend.dll", "Burst.Compiler.IL.dll", "burst-llvm.dll", "Smash.dll" and possibly the "Cecil" DLLs.
