This video has some very helpful instructions and tips to bring some more specific methods to do what has been described in this thread.

I'm extremely grateful to everyone who has had a go at trying to be helpful.

I do think there is something either very Zen or very funny about the collection of answers, which I've tried to summarise here for a bit of light relief as this thread makes me chuckle. So let's start with the original question:

"How do you know when to stop stretching milk?"

Barista Bob tells me to chill my pitcher (knowing it's not what I asked for)

Just a couple more things (like you need more). I always chill my pitcher in the refrigerator so that its temp is the same as the milk, around 40F. Second, only bring it out of the refrigerator when you are ready to steam. Third, get that tip as soon as possible into the milk and start tearing and hold it as still as possible except to move the pitcher slightly down (to inject more air), or slightly up (to integrate the air bubbles).

Mathof tells me you stop when you have enough experience to know when to stop:

By experience. Like many things espresso related, rules are only guidelines that must be varied in practice to suit your desires, your materials (eg, milk) and your equipment.

Beans+Crumble tells me that you should stop stretching before it's too late:

As a note: I believe the concept is to do whatever the amount of stretching you want BEFORE the pitcher reaches body temperature not stretch UNTIL it reaches that temp. All of this, of course, is dependent on the power of the machine's steam wand.

Deephaven tells me that it happens really quickly:

The stretching phase is extremely short if you have any sort of steam power. I have a Decent and many complain it doesn't have enough power but at almost the lowest setting the stretching takes literally less than 5 seconds. I stretch until it resembles paint. At that point it is time to integrate and that portion takes another 20 seconds or so.

Milligan tells me it depends on your machine, but you'll definitely know when you've learned it which takes time:

It is wildly dependent on the equipment. On my old Breville Barista Express I'd stretch for a good 10-15s. On my GS3 I barely blip a little air in and that is it. The difference with my GS3 is more about how aggressively I aerate much more so than how hot I let it get. As can be seen by my previous posts it took a lot of practice to get it right. Now it is all about the feel. I used a thermometer for a long time but now I just feel it out. Takes time.

HB tells me that it depends on the drink, but you definitely need to finish before you get to body temp:

Not to state the obvious, but it depends on what drink you're making. Stretching = adding air = more volume => depends on the drink. Traditionally, lattes have a whisper-thin layer of foam and cappuccinos have a good 3/4" of foam. Of course, you can tweak these to your preference. I agree with prior posters that whatever the desired volume of foam, the air-injection phase should be completed prior to the pitcher exceeding body temperature, otherwise you won't have enough time to swirl the milk into integrated microfoam and break any errant bubbles.

iploya at least is roughly on target and raises the question of wand depth

+1. The moment you can start to feel the warmth is when it has reached body temp. The moment the pitcher gets uncomfortably hot, it is just right for drinking. How much stretching occurs during that first window depends on wand depth, which is easy to say but harder to perfect (we all struggle with it).

Last but not least, Moka 1 Cup tells me he goes for all the foaming he can lay his hands on, but he doesn't actually do latte art

I use a Breville Dual Boiler that even at maximum power is moderate, which I like. I stretch until the milk has doubled in size. That takes enough time to allow the temperature to almost the right value as well. I finish by lowering the wand to the bottom.
However I don't make art, just cappuccino so I am not sure if this answers your question.

I think my conclusion is that I should go and get a Barista Class otherwise my quest for better latte art will forever remain like the Zen riddle of imagining the sound of one hand clapping! Thanks everyone for trying to be helpful on what turns out is a trickier question than I realised when I asked it!

A great conclusion! What seems to be easy when starting out ends up being a hair pulling experience for many. A hands-on barista course is the best money spent. Better than any special tamper, fancy gadget, or upgraded machine. The answer to your question is, there isn't a discrete amount of time that we can throw around. Only tips as you find out what works with your machine and, more importantly, your expectations.

Agreed with the above comment that taking a class can be very valuable... being able to learn hands on with a real person vs watching online videos make a huge difference. I recently took a latte art class, not to improve my latte art, but with the goal of really focusing on improving my milk texturing. I spent 2.5 hours steaming pitcher after pitcher with feedback from the instructor. Extremely helpful and, for me, money well spent. Good luck and post an update to let us know how it's going!