Recently i got a ds lite, which its upper screen flex broken, and i did disassemble it. I would like to share the info I got, so that maybe it could be useful.
After removing the upper screen you will realise there are few things that has been soldered to the flex: speakers, backlight of the lcd and a ground copper to the backplate of the screen. First you need to desolder these, because they are easy to break, especially backlight flex.
Next you will realise that flex cable is coming out of backplate, which has been put together with strong two sided adhesive tape. To remove the backplate, easiest way is inserting something like a screwdriver into the lower right corner. Be careful though, flex cable is extending till around the bottom center. Also there is another backplate, which you shouldn't meddle with. Try to make sure its intact.
Once you removed the backplate, you will see the half of the flex is taped to the back of the lcd. Gently remove the flex from the lcd. You will realise that flex is folding into the front of the lcd.
In the front of the lcd there is a plastic cover, which put together with adhesive. Gently remove the plastic. You will be left with lcd's front plate.
At this point, you should take off the front plate through notches. There will be a black tape at the bottom of the screen covering flex cable. Just remove that tape, and you are left with flex cable's connection to the lcd.
Now, if you come this far without a problem, be extra careful. The flex seems like it has adhesive, and can be removed like a tape. However, if you don't use a constant gentle force through out, some resudue of the flex may stuck at lcd's board. I had this problem, and couldn't remove the resudue later on.
Happy ending. You succesfully removed the flex. I don't have the flex replacement so i didn't put it together, but to put it back you gotta follow the steps backward. Be cautious though, you remove some parts irreversably. For example, black that was on top of flex cable. You may need more than just the flex you got.
PS: I may add some images later, but i didn't took much photo and they are not high quality.