How do I amend form data before it is saved for a custom post type

save_post is much too late to modify the $_POST data itself and hope to have it populate to the post save actions (and modifying $_POST is usually not necessary anyway). The post has been saved at that point. Just check the source.

What you should probably be doing is saving your data to the database explicitly using update_post_meta.

Something like this:

function geocode_clinic($post_id ) 
{
if($_POST['post_type']=='clinics') 
{
    $address = urlencode($_POST['fields']['field_52ea48969a9f2']);

    // geocode the address
    $location = json_decode(file_get_contents("http://maps.google.com/maps/api/geocode/json?address=".str_replace(" ", "+", $address)."&sensor=false"));

    if ($data->status=="OK") {          
        $lat = $data->results[0]->geometry->location->lat;
        $lng = $data->results[0]->geometry->location->lng;
    } else {
        $lat = $lng = '';
    }

    update_post_meta($post_id,'field_52ea4b66b382f',$lat);
    update_post_meta($post_id,'field_52ea4bccb3830',$lng);
}
}
add_action('save_post', 'geocode_clinic');

I am not sure those are the key names you want but that is the idea.