It would make more sense to use an actual submit button in the form instead of a hyperlink that acts like a submit button. You can use <input type="submit"> or <button type="submit"> if you want more control over display/formatting.
If you are set on using a non-submit button (like your hyperlink), then it would be best to give the form its own ID:
<form method="post" id="frm_no_kids" name="frm_no_kids" class="getstarted" action="step1.php">
<input type="hidden" id="price_value" name="fee" value="<?php echo encrypt(499); ?>">
<input type="hidden" id="divorce_type" name="divorce_type" value="no_kids">
<a class="btn border-btn yellow-btn started-hover" title="Get Started" href="javascript:document.getElementById('frm_no_kids').submit();">Get Started </a>
</form>
As was mentioned in the comments, using an event listener is MUCH better:
HTML:
<form method="post" id="frm_no_kids" name="frm_no_kids" class="getstarted" action="step1.php">
<input type="hidden" id="price_value" name="fee" value="<?php echo encrypt(499); ?>">
<input type="hidden" id="divorce_type" name="divorce_type" value="no_kids">
<a id="frm_no_kids_submit" class="btn border-btn yellow-btn started-hover" title="Get Started" href="#">Get Started </a>
</form>
JS:
document.getElementById("frm_no_kids_submit").addEventListener("click", function(){
document.getElementById("frm_no_kids").submit();
});