How do you spare Photoshop Flowey?
Solution 1:
You cannot. You must deplete his health entirely, after gaining the support of the other six SOULs as described here. Then, he will turn back into regular Flowey after a brief cutscene, and
you will be offered an opportunity to spare him. You have to spare repeatedly, because like Toriel, he does not immediately accept your mercy. If you keep sparing, he will eventually "run away."