It's possible that the mobi converter or reader does not like a <br> just at the beginning of a paragraph, try this:
<p> <br>This paragraph has no indent.</p>
...but going back to proper CSS formatting, doesn't the following work the same?
<p style="text-indent: 0">This paragraph has no indent.</p>
if you are going to modify the text to add the <br>, you could just as well add the style="text-indent: 0".