To promote your FeedBurner feed on your Wordpress site, just use FeedBurner's Publicity Tools to select a "chicklet" image to display a link to your feed from your blog's homepage.
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Click the Publicize tab.
A list of publicity-related services appears.
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Locate and click the Chicklet Chooser service.
The form shown below loads into the right side of the screen:
This form contains several options for buttons that promote (and link to) your FeedBurner feed.
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Click the radio button next to the button you want to display on your site.
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Copy the HTML shown in the bottom section of the Chicklet Chooser. You will paste this HTML into your WordPress site template.
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From the WordPress Dashboard, click the Presentation tab and then the Sidebar Widget option.
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Drag the text widget from the Available Widgets area to your Sidebar.
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Click the right side of the widget to expand it
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If you'd like to give this widget a title you can, but it is not required. This title will show up on your site.
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Paste the code you copied from FeedBurner in an earlier step into the content field.
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Click the "X" in the upper-right corner to close the widget box.
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Click Save Changes.
After the code is saved, you should immediately be able to view your chicklet in your site's sidebar.