While Reid Miles’s signature is clearly on this cover, several sources also credit the design to Andy Warhol who worked on a few jazz covers in the 1950s during his career as a commercial artist. The disctinctive Warholian lettering is evidence that he played a role. But Warhol often asked his mother, Julia Warhola, to add her signature calligraphy to his work, and the lettering here is very close to her well-documented handwriting for The Story of Moondog. So you could make a case for crediting all three individuals for this great cover. Incidentally, several digital fonts seek to emulate the Warhols’ lettering. FF Pepe may be one of these.
“MONK” (likely wood or photo type) is perhaps Tempo, not Futura. The tip-off is that Tempo is clearly used on the reverse side of the sleeve — see the distinctive Heavy ‘K’. Vogue is used for text on the back. The two typefaces also have a long history on Blue Note records.