Conditional for Post Format

There is no “default” post format type, though internally in core, a post that has no post format assigned is usually referred to as standard. So, your first conditional will return false using post-format-normal because there is no such post format – but would still return false using post-format-standard.

You could reverse the conditional, and check for gallery post format first. Note that you could use either 'gallery' == get_post_format() or has_post_format( 'post-format-gallery' ). (Personally, I find get_post_format() to be a bit more intuitive.)

In any case, you would reverse the conditional like so:

if ( has_post_format( 'post-format-gallery' ) ) {
    flexslider('index-post-image');       
} else {
    // Fallback output here
}

Note that you also have syntax errors in your code, such as nested PHP tags.