FolioVision

Feedburner was a great service. It’s a bit of a mystery why Google is shutting down Reader and why they dropped support for Feedburner and shut down its API. Both were popular services and offered Google valuable content intelligence. The shutdown is a real wakeup call to those of us who depend on external services.
Since Feedburner is no longer supported, we created this plugin to help you migrate your subscribers and to allow you to keep your feed on a URL controlled by you going forward. You will be immune to feed companies going out of business, shutting down services or hiking prices in the future. Take control of your own feed and your own subscribers!
Benefits:
<ul>
<li>Boost number of your newsletter subscribers by putting subscription form to your feed address</li>
<li>Keep your Feedburner RSS readers! When Feedburner subscribers come to your site, they will automatically be prompted to re-subscribe on your new feed address when they read the feed</li>
<li>Upgrade RSS readers to email recipients. Show a subscription form for your Feedburner subscribers when they come to your website.</li>
<li>Easy to set up and get started: built-in newsletter subscription form works out of the box</li>
<li>Default subscription form works with <a href="https://wordpress.org/extend/plugins/newsletter/" rel="ugc">Newsletter</a> plugin by Satollo and uses double opt-in (confirmation emails)</li>
<li>Optional CSV export for subscribers who sign up before you add your own mailing solution.</li>
</ul>
Never pay monthly fees no matter how many subscribers you have. Never risk losing your subscribers again.
<a href="http://foliovision.com/seo-tools/wordpress/plugins/fv-feedburner-replacement/" rel="nofollow ugc">More Information</a>
<a href="http://foliovision.com/support/fv-feedburner-replacement/" rel="nofollow ugc">Support</a> | <a href="http://foliovision.com/seo-tools/wordpress/plugins/fv-feedburner-replacement/changelog/" rel="nofollow ugc">Change Log</a> | <a href="http://foliovision.com/seo-tools/wordpress/plugins/fv-feedburner-replacement/installation/" rel="nofollow ugc">Installation</a>

FV Feedburner Replacement

Creates a landing page for your feed subscription and out of the box working newsletter subscription form.

Md Abul Bashar

Just use Feedburner Email Subscriber service on your website sitebar widget.
Full <a href="http://www.codingbank.com/item/wp-feedburner-email-subscriber-wordpress-plugin/" rel="nofollow ugc">Documentations</a>
You can watch this videe 
https://www.youtube.com/watch?v=lqQnR_21UvQ

WP Feedburner Email Subscriber

Does the job

Just use Feedburner Email Subscriber service on your website sitebar widget..

FV Feedburner Replacement vs WP Feedburner Email Subscriber