Hi,
Indeed, you are in a special case. My previous answer was towards the general use case since I didn't know the specifics of your website.
The flushing of the cart after the order is processed is already what is done by default in HikaShop. After you go back from the payment gateway, the cart is flushed.
However, in your case, since you don't use a payment gateway, it's probably why it doesn't happen. But that can be changed. Just set the option "Clean cart when order is" of the configuration to "created" and the cart will be flushed directly at the end of the checkout. No need for custom development for that.
That should be already enough to take care of your issue since the users would have to re-add the products to the cart in order to process the cart again through the checkout, which would serve as a delay. So I would first recommend to try that and see how it goes. But then, if you need such delay implemented, adding a flag in the user session to forbid the creation of new orders for 3 minutes should be easy to do for a developer with a small HikaShop plugin. So yes, our partners, or any other Joomla developer, should be able to help you with that.