You heard taxes are lower in the Canary Islands, therefore you want to shop here, great idea!
In Maspalomas, Yumbo is great for gay shopping (underwear, swimwear and fetishwear by ES Collection, Boxer, etc…). Also in the stores Dress Code and Why Not? you can find the brands TOF Paris, Pump!, Modus Vivendi, Andrew Christian and more. For everything else, it is best to go to normal shopping streets and malls below.
You also have the shopping boulevards of Meloneras (El Faro Boulevard and Oasis Beach Boulevard) where you can find the official stores of designer brands such as Hugo Boss, Ralph Lauren, Tommy Hilfiger, etc… And for shoes, Aldo is always a great choice.
15 minutes West of Maspalomas, you have a bigger shopping center called Mogan Mall in Puerto Rico with several official big brands stores (Timberland, Levy´s, Bershka, Lacoste, Pull & Bear, Vans, GAP, etc…).
There is also Atlantico in Vecindario (15 minutes north of Maspalomas), which worth noting has a nice modern movie theater with movies in English (look out for the indication “VOSE”) every Tuesday.
30 minutes North of Maspalomas in Las Palmas, Alisios is the best mall of the island, a very nice, big, modern and complete shopping center, followed by Las Arenas. Than you have the outlet mall Las Terrazas. There´s also El Mirador another mall if you have visited all of the other malls and you want to visit all of them (or want to go to Primark).
There´s also the main shopping street in Las Palmas called Triana which is a very long street with big known brands, as well as its surrounding area . Most side streets branching off the main street often have shops worth looking at too.
Find everything here.