How to restrict “too soon” downloads with a general rule?

You should implement cookies.

In js file, you have to write a click handler for Load button. In handler, you should check if cookie is already exists. If not, you need to create cookie containing current time and allow user to proceed (propagate click event).

If cookie exists, compare current time with time stored in cookie. If interval is less than 15 sec, block click (preventDefault(), return false).

If interval is more than 15 sec, update cookie and allow further execution of click event.

This is the skeleton of algorithm to solve your task. If you have some experience in javascript, you can create this piece of code by yourself. Otherwise it is better to hire a developer.