OK. I got things working by changing up the way I do things.
Now I have a new little issue!
My form keeps duplicating submissions on refresh?
<form action="<?php the_permalink(); ?>" method="POST" enctype="multipart/form-data">
<input name="test_field" value="" required/>
<input type="submit"/>
</form>
<?php
$post_id = 291;
$field_key = "test_repeater";
$row = array(
"test_field" => $_POST["test_field"],
);
add_row($field_key, $row, $post_id);
?>