Flower and flour are said to be homophones. However, considering the number of different pronunciations (/flaʊə/ like BrE sour, /flou(-ə)r/ like AmE sour, /flɑː/ (forvo) like BrE car, etc.) floating around, are they always homophonous for each particular speaker?

Edit: As tchrist points out in the comments, the same question could be asked of dower and dour.