I've always thought that vanilla and espresso would be a good combination but the problem is: I don't take sugar! I understand one can buy coffee flavoured beans but how would I get the vanilla flavour using my home set up (espresso machine, burr grinder and preferred brand of beans)?
You just add any vanilla-tasting product to your coffee. It doesn't have to be a sugared "coffee flavor".
The best option should be plain vanilla extract. Then you have synthetic vanilin, which comes as a white powder or in tiny vials of propylene-glycol solution. As it is very concentrated, it ends up being much cheaper than the extract, but its smell is nowhere as rich as that of real vanilla extract.
I suppose that you could also use real vanilla pods. I would cut off a piece, cut it open, and place it within the ground coffee during brewing (if you think it will interfere too much, you can also just scratch out the seeds and use them, but you will be throwing out lots of vanilla that way). I have never done it, so I don't know how big a piece you will need for the taste to be reasonably strong. I suspect that using vanilla extract will be more economical, as vanilla usually needs time to give off aroma, and the short espresso brewing time, even with the pressure, will need a fairly large chunk to make a difference in taste. Still, the pressure-brewed vanilla will have a different taste profile than the alcohol-dissolved vanilla extract, so if you are not happy with the taste the extract gives, this is one more method to try out.
I would add the vanilla to the espresso after brewing it.
You can use vanilla extract (liquid or in powder) or real vanilla pods.
Adding any of them to the coffee beans would be a pity for your grinder (if you have a good quality grinder, as an espresso deserves).
Adding vanilla pods or seeds to the basket would affect the microchannels, as probably the synthetic extract would do. Also, extraction time must be very precise to extract the coffee tastes, and we would be lucky if they coincided.
The answer @JoeFish gave in his comment is very interesting, as coffee is known for absorbing odors. But it should be experimented to check if those aromas get extracted with espresso brewing.
Just brewed espresso is about 70C/160F, infusing vanilla pods for 3 or 4 minutes will give it some flavor, and you can reuse the pods several times. If using vanilla extract, it dissolves in water, so you can also add it after brewing.