Feedburner statistics are not part of Google Analytics and I couldn't understand why but you can track Feedburner Email Subscription Form Submission in Google Analytics Very easily.
Activate Email Subscription for your Feed in Feedburner and grab the HTML code of your subscription form. The HTML code should look like this.

Now insert the onclick handler code for submit button to track form submissions in Google Analytics. The onclick event handler code is
So
Becomes
Tracking works with the latest code of Google Analytics and you can see the tracking in action for my blog in the screenshot below.

If you have multiple forms on a page and want to track submissions of each of them separately you can either change the tracking string like
or like
If you have any queries or questions, do share them in comments below.
Activate Email Subscription for your Feed in Feedburner and grab the HTML code of your subscription form. The HTML code should look like this.

Now insert the onclick handler code for submit button to track form submissions in Google Analytics. The onclick event handler code is
HTML Code:
onclick="javascript:_gaq.push(['_trackPageview','/formsubmission/feedburner']);"
HTML Code:
<input type="submit" value="Subscribe" />
HTML Code:
<input type="submit" value="Subscribe" onclick="javascript:_gaq.push(['_trackPageview','/formsubmission/feedburner']);" />

If you have multiple forms on a page and want to track submissions of each of them separately you can either change the tracking string like
HTML Code:
onclick="javascript:_gaq.push(['_trackPageview','/formsubmission/feedburner-sidebar']);"
HTML Code:
onclick="javascript:_gaq.push(['_trackPageview','/formsubmission/feedburner/sidebar']);"
HTML Code:
onclick="javascript:_gaq.push(['_trackPageview','/formsubmission/feedburner/afterpost']);"