Get referral (parthnership) link for a product on Aliexpress?

The question is about API and independent from programming language.

I want to get a commission from products on Aliexpress.

API documentation (press "API Documents")

But I can't understand how to generate a link and then how to check if it is correct.

As I understand I need to use 1.1 listPromotionProduct request, get all the links from the result and apply 1.3 getPromotionLinks to them. Is it correct?

Yes you're right this is the way to do it, so you need to do two API calls, one to api.listPromotionProduct, collect up the URLs and then make a call to api.getPromotionLinks.

This URL works:

http://gw.api.alibaba.com/openapi/param2/2/portals.open/api.getPromotionLinks/YOURAPIKEY?fields=totalResults,trackingId,publisherId,url,promotionUrl&trackingId=YOURTRACKINGIDHERE&urls=https://www.aliexpress.com/item/Rotary-Cheese-Tools-Cheese-Grater-Stainless-Steel-Slicer-Shreds-Drum-Hand-Held-Ginger-Graters-Cutter-Kitchen/32706493641.html

Append more URLs to this URL using a comma (up to 50 URL's).

Likely Issue

The thing I was doing wrong was using the wrong trackingID, it's not your digital signature but the affiliate ID you specified in https://portals.aliexpress.com/publisher_manage.htm (I think you can have multiple affiliate ID's).