I figured it out. If anybody needs to know I added the below snippet at the end of the product loop on the archive template. The file name was ‘content-product.php
<form class="form-inline cart" method="post" enctype="multipart/form-data">
<div class="form-group wc-donation-amount">
<label class="sr-only" for="exampleInputAmount">Amount (in dollars)</label>
<div class="input-group">
<div class="input-group-addon">$</div>
<input type="text" class="form-control" placeholder="Amount" name="donation_amount" value="0.00" id="donation_amount_field">
<input type="hidden" name="add-to-cart" value="<?php the_ID(); ?>">
</div>
</div>
<button type="submit" class="single_add_to_cart_button button alt">Donate Now</button>
</form>