According to DMOZ editors who have posted on other forums there are basically two schools of thought on this.
There are some very strict editors who won't allow any sites with any affiliate links. There are other editors who feel content is the important factor in determining the worth of a site to DMOZ.
The DMOZ standard is content, unique above all, whether it contains affiliate links or not is irrelevant. The sites are supposed to be judged as if there were no affiliate or outside links at all. Would the site stand on its own as a good content site with uniqueness? If so, it should be included, if not, it should not be included.
We all know that DMOZ has its share of poor quality sites ... some even with nothing but affiliate links and no unique content. Some domains were bought out and replaced with less than quality content. It happens. Nothing we can do about that.
However, if your site has quality content with a unique view/presentation or other factor that makes it different, then affiliate links should not stand in your way.
If your site gets rejected, you can post at the DMOZ forum requesting more info, you can also ask the status of your submission 4 weeks after you have submitted (not before!). It might do you well to browse the DMOZ forum and get a feel for what you are up against. Some categories haven't been updated, and sites have been queued for over 6 months ... patience is a virtue at DMOZ
The url for the forum is: