Open Chronaria and go to Settings → Account → Delete account. The deletion is immediate: nobody has to approve it and there is no waiting period.
If the app asks you to sign in again first, that is not a fault: Google refuses to delete an account on the strength of an old sign-in, because somebody who found an unlocked phone should not be able to close its owner's account. Sign in again and repeat it.
If you have uninstalled the app, lost the phone or cannot sign in, write to dreamsin03@gmail.com from the email address you registered with, asking for the account to be deleted. The request is carried out without undue delay and in any case within 30 days, and you will get a confirmation when it is done.
If you write from an address other than the registered one you will be asked how you can show the account is yours: it is the only way to stop a stranger having somebody else's data deleted.
Everything that concerns you, permanently:
The news articles downloaded from the feeds. They are stories published by news organisations, shared by every reader, and they contain nothing about you: neither your identifier nor the record that you had read them — that goes with the account.
The technical server logs, which contain the IP addresses of requests, are not deleted on request: they rotate and overwrite themselves within a few weeks, and they are not linked to your account.
If you have an active subscription, deleting the account does not cancel it: subscriptions are managed by Google and are cancelled in Google Play → Subscriptions. Do that before deleting the account, or you will keep paying for a service you no longer use. One-time purchases have nothing to cancel.
There is no bin and no restore. If you want to come back you start from a new, empty account: the reports written in the past do not come back.