I want to add the FeedFlare code into the header section but since it contains php code I am not able to do it.

Here is the code that google generated to be added:
<script src="http://feeds.feedburner.com/~s/---/---?i=<?php the_permalink() ?>" type="text/javascript"></script>

I can add a script through 'Add HTML/CSS Insert' option of the ATO but it does not allow the imbedded PHP code. Would appreciate any help. Thanks.

You may have to add the code to index.php or perhaps there is a plugin that will help you with this.

or add a new widget area to the header configuration section and put the code in a php aware text widget

Adding a widget area in the header configuration looks interesting. However, I took an easier way out and installed Flare Smith plugin. If that does not work then I will revisit adding widget area solution. Thanks.