If what you are trying to do is pre-populate the text input, it looks to me like you need to echo the $zip_code variable you are creating:
<input type="text" name="zipcode" placeholder="Zip Code" value="<?php $zip_code = mo_baptist_get_meta('street_zip'); echo $zip_code ?>" />
other than that, I also noticed that the text input was not closed – I added that in the above example…