Create unique identifier that is displayed to the user and admin via Ninja Forms

Put this code into theme’s functions.php: ( for Ninja Forms 2.9.x )

function unique_code_submission( $data, $field_id ) {
    global $uniqueCode;

    if ( "string" !== gettype( $uniqueCode ) )
        $uniqueCode = uniqid();

    /* here goes your code to populate a field */

    return $data;
}
add_filter( 'ninja_forms_field', 'unique_code_submission', 10, 2 );

Within above function you will have a unique, 13 characters long code in $uniqueCode global variable. This code will be generated once only, when the filter is triggered first time. More information about ninja_forms_fieldfilter: here.

UPDATE: for Ninja Forms 3.0 and up:

function unique_code_submission( $fields ) {
    $uniqueCode = uniqid();

    /*  here goes your code to populate a field. For example:
        let's populate hidden field, which has key value of
        'hidden_1492812363939' */

    $index = 0;
    while ( 0 <= $index ) {
        ++$index;
        if ( 'hidden_1492812363939' == $fields[ $index-1 ][ 'key' ] ) {
            $fields[ $index-1 ][ 'value' ] = $uniqueCode;
            $index = -1;
        }
    }

    return $fields;
}
add_filter( 'ninja_forms_display_fields', 'unique_code_submission', 10, 1 );