I am looking to take a few lamp shades on a KLM flight to Amsterdam and, from there, on to Delhi.
Do I need permission from KLM to take them in the cabin, or I can take them with me when I board?
First, Give KLM a call and ask them for guidance.
The problem with taking them with you as carry on is that you will need to put them somewhere (overhead bins), and make certain other passengers will not crush them when the put their own stuff in the bins.
Do the lamp shades stack up or they are separate items ?
I'd find a suitable box and pack them with bubble wrap and packing popcorn and put a large "fragile" sticker on them and check them in as regular items.