There is a SmartObject called Escalations Report in the System => Reports category (you will need to turn on show System Objects if you are accessing through the designer).

It takes a Process Instance Id and optionally an Activity Instance Id and Event Type.  You can get the Process Instance Id from the start of the serial number and could then filter a call to that list method with the username if needs be.

Cheers

There are a couple of options available to you here:
1. You can call a SmartObject when the task is redirected and log some information in addition to doing the redirect. When the task is opened by an escalation recipient you could then act on this logged data.

2. Instead of using the redirect functionality to escalate the task, the original one could be expired and you could create a new task for the escalation. With this option you can log whatever information to your database that you want to in the escalation task include any information in this task about the escalation that you need to.