Please note that the hidden orders would not be removed from the account. It will not appear under the Returns & Orders section but would still be visible if you visit the account page and then tapping on Account & Lists>Archived Orders. All the archived orders will be available there. In case, you want them back on the main list, click on the Unarchive Order button present next to the product(s).
How to Delete Browsing History?
Be sure from every corner if you want to hide your purchases. That means deleting your browsing history too since if anybody has to check that they will know what products you were looking into and possibly bought them too. To delete browsing history go to Your Account>Account & Lists>Browsing History>Remove from View the product name you want to delete. You can also click on the Manage History>Remove all items from view.
Stop Alexa
You need to be more aware if you use an Echo device as Alexa would automatically update on deliveries even if you hide the purchase history. Do this additional step if using the device:
