I have resigned TCS . Have 13lpa offer in hand from Congnizant and now having HR round with American Express ka.Can I ask hike of 30-40

Yes, if 30-40 is the salary range for this position in American Express then go for it, as you have a good backup.
Between what's YOE?

I think it is better to ask for something in range of 20s first...my views only...All the best😊

I would suggest brother go to leetcode compensation section there I have seen many anonymous comp discussion of American express and try on blind as well. What is your tech stack on which you are switching?

How much notice period Cognizant agreed ?