Here's what works (some of the time) on the website I use:
http://www.klm.com/de_en/index.jsp
Warning: Other websites may not work the same.
Anyway:
1. After you get rid of the pop-ups, go to the left-hand side and click on "Flying Dutchman".
2. This will cause a drop-down (expansion) menu. Click on "Award Booking".
3. This brings up some choices in the right-hand frame. Way at the bottom is "Miles Finder". Click on the "read" link.
4. This, for unknown reasons, cycles you out and requires you to log into your account. I've never been able to figure out the (alleged) thought process here - are the awards differently priced for different members?
5. After you've logged into your account, you will (sometimes) be brought back to the "Miles Finder" page. Other times, you will not. In that case, dispose of any pop-ups and start over from step 1, above.
6. For unknown reasons, this link
still won't give you a chart. It requires that you enter your origin and your destination and then will give you a limited chart for that region-pair only.
I know, it makes no sense to me to do it that way, but it apparently made sense to whomever laid out and approved this process. I have no idea why they don't have a mileage chart that can be accessed with one (or at the most two) clicks, like the other major airlines do.
If anyone knows of a shorter way, or one that gives you the entire chart (all regions), please post here.