Pass PHP through redirect and custom fields

Without touching rewrites – you could probably do somthing like

website.com/?goto-amazon=<?php echo get_the_ID() ?>

Which’ed output

website.com/?goto-amazon=42

Where 42 is an example of a post that contains the amazon_keywords.

In your site you could listen for the goto-amazon query and redirect thereafter

add_action( 'init', function(){
    if (isset($_GET['goto-amazon'])) {
        $keywds = get_field('amazon_keywords',intval($_GET['goto-amazon']));
        $link = "http://www.amazon.co.uk/s/?_encoding=UTF8&camp=1634&creative=19450&field-keywords={$keywds}&linkCode=ur2&tag=AFFID";
        wp_redirect($link);
        exit;
    }
});

UPDATE

To do with rewrites you could so something like so. On your post

$url = get_site_url();
$id = get_the_ID();
echo "<a href="https://wordpress.stackexchange.com/questions/290264/{$url}/goto/amazon/{$id}/">go to Amazon</a>";

Which’d make a link like

website.com/goto/amazon/42/

Then in your functions

add_action( 'init', function(){

    // uncomment reload once or twice, or hit SAVE in wp-admin > Settings > Permalinks
    //flush_rewrite_rules();

    add_rewrite_tag('%gotoamazon%','([^&]+)');
    add_rewrite_rule('^goto/amazon/(.*)/?','index.php?gotoamazon=$matches[1]','top');
});


add_action( 'template_redirect', function(){
    global $wp_query;
    if ($goto = get_query_var( 'gotoamazon' )) {
        $keywds = urlencode(get_field('amazon_keywords',intval($goto)));
        $link = "http://www.amazon.co.uk/s/?_encoding=UTF8&camp=1634&creative=19450&field-keywords={$keywds}&linkCode=ur2&tag=AFFID";
        wp_redirect($link);
        exit;
    }
});

When dealing with rewrites, make sure you reset the rewrite rules, instructions in commented code above.

I don’t know how amazon expects the keywords, but they should be urlencode()‘ed

UPDATE

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