Puree the chili powder, pepper flakes, and pimentón de la Vera with the olive oil in a blender until completely smooth. Put the mixture in a saucepan and bring to a simmer over moderate heat. Simmer for 45 seconds, then set aside to infuse for 10 minutes. Pour through a fine-mesh sieve into a bowl. Don't press on the mixture, but you can tap the strainer against your hand to get the oil to drip through faster.

Now strain the oil again through a flat-bottomed paper filter. If the filter clogs, you may need to change the filter partway through. It's okay to pick the filter up and squeeze it gently to force the oil out faster, but take care not to break the filter. Store in an airtight jar in a cool, dark place. It will stay lively for at least 1 month.