How can the Feeds module fetch a file from a dynamic URL?
As I know Feeds doesn't have something like that, its maybe a feature that you can propose on they issue list.

A workaround its to create a small module that will work as a proxy for your dynamic address.

You will have something like that : 

&lt;?php

function proxy_menu() {
  $items = array();
  $items['proxy-url'] = array(
    'title' =&gt; 'Proxy for danymic url',
    'page callback' =&gt; 'proxy_get_contents',
    'access callback' =&gt; TRUE,
    'type' =&gt; MENU_CALLBACK
  );
  return  $items;
}

function proxy_get_contents() {
  $url = 'http://www.example.com/report/%start-date%/%end-date%';
  $request = drupal_http_request($url);
  if ($request-&gt;code == 301 || $request-&gt;code == 304) {
    return $request-&gt;data;
  }
}