Don't forget 'Family Man'!
Aston Barrett gets the ultimate Jazz + flats tone, to my ears. An astonishing combination of hugeness and clarity, with extraordinary dynamics and an upright-ish attack and note shaping. He uses Fender flats exclusively.
Robbie Shakespeare, of course. He uses Dean Markley flats, and always has. Another tone monster, and family Man's protégé, who helped define the sound of reggae bass.
Also Jackie Jackson, Boris Gardiner, Lloyd Parks, George 'Fully' Fullwood, Cinton Fearon, Leroy Sibbles, Errol 'Flabba' Holt, and countless other reggae bassists get their sound from flats.