I have created a website(http://www.filleritem.com) and am looking for
ways to promote it. I have submitted to dmoz.org, but am looking for
other specific free ways to promote my site. Preferably sites/forums
where people are interested in getting free shipping from Amazon.com.

you can sing up at http://www.trafficswarm.com to promote your website

I am not looking for sites like trafficswarm.

DMOZ normally does not list affiliate web sites. Are you looking to
hire a company/someone for the promotion or are you looking for forums
where you can put your site in the signature, link exchanges etc.?

try www.ediamondstudios.com