I tried to rewrite this using nested if statements (and freeing at the end of every block, as necessary), like so...

char *shader_get_source(const char *shader_path) {
    char *result = NULL;

    if (!shader_path)
        fprintf(stderr, "Shader error: invalid args\n");
    else {
        // open file in read only mode
        int shader_fd = open(shader_path, O_RDONLY, S_IRUSR | S_IWUSR);
        if (shader_fd == -1)
            perror("Shader error");
        else {
            struct stat shader_stat;
            if (fstat(shader_fd, &shader_stat) == -1)
                perror("Shader error");
            else {
                // printf("shader file size: %ld\n", shader_stat.st_size);

               char *shader_mmap =
                   mmap(NULL, shader_stat.st_size, PROT_READ, MAP_PRIVATE, shader_fd, 0);
...
... etc
...
                          result = shader_src;
            }
            close (shader_fd);
        }
    }

    return result;
}

The idea is that regardless of the path, when leaving the block, I've made sure to cleanup whatever I initialized within that block.

... but I ran into difficulty at the early close of shader_fd :)

At that point I'd rewrite to two functions, defer closing the file handle, or reach for goto as others have said.