How to call a post’s metadata in shortcode.php?

The first one doesn’t work because $post doesn’t exist inside the context of your shortcode function, you would need to add global $post; before it. However…

You should use get_the_ID() instead of accessing the $post global directly. The reason it doesn’t work in your second example is that it’s not a class method, it’s just a function, and $post is just a simple object (plus, it doesn’t exist anyway! you have the same problem as the first version above).

Always develop with debugging enabled and your blank white screen will then show error messages to tell you what’s wrong.

So, the working version should be:

get_post_meta( get_the_ID(), 'destination', true );