Getting email feedback via PHP form in different file [duplicate]

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• Reference - What does this error mean in PHP? 27 answers

I'm looking to implement a feedback form on a website I'm making and am running into problems when I try to separate the PHP mail script from the HTML where the form resides. Here is my PHP script:

<?php
        $mail_to_send_to = "......@gmail.com";
        $your_feedbackmail = "...@...coffee";

        $sendflag = $_REQUEST['sendflag'];
        if ( $sendflag == "send" )
        {
                $email = $_REQUEST['email'] ;
                $name = $_REQUEST['name'] ;
                $message = $_REQUEST['message'] ;
                $subject = $_REQUEST['subject'] ;
                $headers = "From: $your_feedbackmail" . "\r\n" . "Reply-To: $email" . "\r\n" ;
                $a = mail( $mail_to_send_to, "Feedback Form Results", $message, $headers );
                if ($a)
                {
                     print("Congratulations, you've successfully entered!\r\n");
                     print("Be sure to 'Like' our Facebook page to complete your entry -> http://www.facebook.....\r\n");
                     print("We will contact you soon with more information :)");
                } else {
                     print("Message not sent! Please contact brett@...com if you see this\r\n");
                }
        }
?>

If I have a simple form in index.html along with my PHP script, the mail sends and the success message prints. However, for structure reasons, I don't want the PHP to be in my large index file. Instead, put it in a file called "submit.php" and declared that as the action of my form:

<form id="contact-form" action="submit.php" method="post" enctype="text/plain">
                <div class="row">
                    <div class="col-md-6">
                        // Fields ommitted
                </div>
                </form>

When I submit a message on the form, no email is sent, and the browser refreshes to a blank "myOriginalDomain/submit.php" site.

Where am I going wrong? Any advice as to what I'm missing is much appreciated.