The second month starts 1 December. 30 November is still the first month. The first day on which you can change your season ticket is 1 December.

If your NS Flex subscription initially started on the 31st, the renewal date is the 1st.

You should be able to switch to Flex Basis on November 30 (because November 31 does not exist) and not be billed the next month.

If you can switch per December 1, you might be billed the full month but wil get reimbursed within a week. Travel on November 30 is of course in the first month.

There is no absolute certainty on which monthly invoice travel costs appear.
Travel data processing times vary.

Even when a NS Flex subscription already terminated, travel costs may appear on a next monthly invoice.

NS Flex subscriptions may start, terminate and switch version at any day of the month, with a minimum period of one floating (not calender) month between changes.

Subscription costs are calculated on a daily basis.

Switch/termination notice time is zero days, so NS Flex really is flexible.

Thank you. Then I’ve got a further question, to be on a safe side.
If I travel on Saturday November 30, and change to say Basis in the evening of that same day after finishing all travel, will that travel remain free or will be recalculated retrospectively as if I have already changed to Basis?  

It will remain free.

thank you. And one more question. 
If I click on subscription change now, I get the following strange message: 
 

“You are unable to change this subscription because you are not the contract owner.

Please contact our customer service for more information.”

What that might mean? 

This message means something is wrong with your Mijn NS account, contact NS Customer Service to have it fixed.

The message should show the webshop or first possible date to change your subscription.

Customer Service has failed to resolve it ) 
Finally, I’ve got my subscription changed via ticket counter in Schiphol. The guy there was very surprised with such a request and struggled finding the needed items in his terminal, but still managed it.