The case for Van Gogh comes from an anecdote reported from his Eindhoven period: during piano lessons he compared the notes to colors, allegedly unsettling his teacher, who is said to have taken it badly. His letters add atmosphere, describing sounds of color and color of sounds in passages that read cross-sensorially.
The case against is method: one secondhand anecdote recorded in the biographical literature, plus letters by a writer whose prose was metaphorically extreme about everything. Retrospective diagnosis of historical figures is unreliable at the best of times, and this is thin material.
He appears on nearly every famous-synesthetes list. The defensible statement is that the claim exists, the primary evidence is a single anecdote, and no verdict is possible. That is where we leave it.