Do AMP holders have to take care in anyway with regard to the upcoming Bitcoin developments (SegWit2x)? Is there any specific precaution I need to take?
I think OMNI has announced that they will stay on the longest chain, thus AMP will be on the longest chain.
So there is nothing to worry about. You should probably not do AMP transactions on the blockchain until Segwit is not active.
Thank you for your response. And is it possible that AMP also splits and runs on two chains? Could a scenario happen similar to Bitcoin holders that might afterwards not only hold Bitcoin Core tokens but also Bitcoin Cash tokens?
No, AMP is on Omni, Omni has no intention to split.
Omni is on Bitcoin, and Omni will go with the longest chain.
So AMP will be on the longest chain of Bitcoin ,so no worries.