I agree with irishguy28. It would be dangerous to do nothing until departure. The ticket is issued and priced as USA-COK. You will probably have problems checking in at the US airport if ticket is invalid for some reason. It can get even worse if that is a return ticket.
I don't know when you are flying, but I can see at least two options:

1. AMEX manages to rebook your BLR-COK segment (and possibly the return COK-BLR). Clearly it does take time. No idea why 6E (or KL) cancelled the codeshare agreement, but the indian aviation sector is in turmoil. BLR-COK is served only by LCCs 6E and IX; it is probable that KL does not have inplace agreements and relations between KL and 6E might be tense. But AMEX should/will find a solution.

2. Reissue the ticket as USA-BLR (and possibly the return). Then you will be on your own for the BLR-COK segment. However that might entail a stiff repricing based on current fares rather than those 6 months ago. A little fight might be needed by AMEX to get KL to use historical fares. The problem is that USA-India is not covered by EC261, so you can only rely on DOT rules.

UNless you are flying in the coming hours/days, Option 1 should clear. Just showing at the airport without the problem solved is a risky endeavour.