Carrying tobacco from US in my suitcase

How much? I would assume not.

No. Unless your suitcase contains nothing other than tobacco.

250 grams tobacco is allowed.

or just over 8 ounces...

If checked bag, no issue, if carry-on, I doubt it would be an issue unless TSA for some reason deems it a threat. As for arrival in Amsterdam, you will go through immigration to have your passport checked, then on exiting, you will see the main door in Green labeled "Nothing to Declare" where you simply walk out, or if you are carrying a large amount (several rolls of a dozen cans) then you may want to wander over to the red "Items to declare" area and declare them, likely paying a duty, but maybe being waved through.

For what it is worth, you will not find chewing tobacco in the EU, I believe there is currently a ban on the sale of it. I do not believe this is a problem for you bringing some in for personal use, only if you bring a large quantity that might be suspected for sale.

Thank you all for your responses. All very good information.

Thanks,
Kelly