Sadly at this time there is no dedicated Route 66 podcasts. But there are a few that touch on 66. The best one I can suggest is a video podcast series produced for the making of the first Cars movie. The podcast chronicals a trip the movies producers and animators took down Route 66 to inspire the movie, and give it an authentic feel. Just look for the Cars: Video Podcast on iTunes.
I have actually come across a few that you as my readers may find helpful in family packing and planning your trips. You can find them in iTunes or at the links below.
This blog link below is for a site called the Domestic CEO
I this particular blog and accompanying website, the host Amanda Thomas gives some great tips on getting your family packed for a trip. Ultimately you have to pack in a way that works best for you and your family, but I think you will find her tips useful.
Another great podcast is from the guys at Road Trip Radio. The episodes are filled with great tips, little side trip ideas, and a lot of usable and sometimes comical information. Just as a warning though the comedy bits at the end are always incredibly corny.