I think you're overcomplicating it. WordPress and AIM use completely different technologies, so there's no straightforward approach to integrate them. Given enough time and money, anything is possible, but if you're looking for a simple, step-by-step solution, you can use an iFrame to create the appearance of an integration without getting involved in a ton of custom development work:
Step 1: Create a new WordPress page.
Step 2: Insert an iFrame on the page, using your AIM URL as the iFrame source
Step 3: There is no step 3, you're done. Anyone who visits this page will be able to view your entire AIM application. Any navigation within AIM will take place within the iFrame, so you don't have to concern yourself with WordPress menus or anything.