How does one who wishes to observe the fast of David fast if their fast happens to fall on a Friday exclusively?

Whoever fasts the fast of Dawud (peace be upon him) — a day on and a day off — incurs no sin by singling out Friday or Saturday for fasting, because he did not intend to dedicate that day specifically. The prohibition is designated for cases where there is a strong overriding reason to fast, such as when it coincides with a day one habitually fasts, as stated in the Hadith in Muslim: "Do not single out Friday for fasting among other days, unless it coincides with a fast that one of you habitually observes."