A COVID 19 vaccin will be available soon. But I don't expect that private doctors will be able to buy it at the pharmacy. All the vaccins will go to the seguridad social. If you are a resident in Spain you will be able to get it at the Centro Salud.
If you are not a resident I think you will have to go to England for the vaccin. If the information changes I will inform you about it on this page.