I have a product receiving the alert that will only accept that format.
Depends on the field in question. Not all date/time fields have the precision down to milliseconds. What field are you talking about?
Best possibility would be to export the Alert to an XML and attach - then we can look at it.
The precision isn't actually that important but the format is. The normal DateTime field would be a good choice, but it will only be used to a date precision. The format needs to be in total numeric count of milliseconds, which is the trick.
Can you provide a screenshot? I'm curious how this would be used in an alert.
I can see that you are a visual person, so am I, so I included a screenshot. But as I said earlier, this alert is being sent to another product that can only handle millisecond timestamps, so it's not directly for human consumption.