If a blog hosted on wordpress.com, then no widget is allowed to be displayed inside the posts.

The only option to run a link party to wordpress.com sites is to add a button which, when readers click on it, takes them to an external page where the linkup is hosted. 

If a blog's installation is on a self-hosted wordpress.org platform, blogger or typepad, the widget will display the linkup inside the blog posts, if the code placed correctly.

To place the InLinkz code properly, simply remove the code you have already added to you blog and grab a fresh copy of the code, as shown below:

If possible, paste it to your blog while in HTML editing mode and do not switch to preview. Just commit your changes.

Wordpress.org is the site that produces and serves the code (the software) for the WordPress blog platform. You can freely get this code and install it to a server/ host of your choice and have a blog that is completely owned by you. This is a self-hosted blog where you set the rules of what works and what does not. And there, you have administrative privileges and install whatever you want.

On wordpress.com (eg myblog.wordpress.com) you have the free stuff without the hassle of setting up a server by yourself. The drawback is that their blog platform has some restrictions, one of which is that you cannot embed scripts or objects.