#1 Monk 11/Rogue 6/Warlock 3 gets 3 ASIs, 3d6 SA dice, 4 skills with Expertise, Uncanny Dodge.
DPSR@20 (Hex as BA) = 2d6+5+2d6+6d6 + 2d6+5+2d6 = 59
DPR@20 (FoB as BA) = 1d6+5+1d6+3d6 + 1d6+5+1d6 + 1d8+5+1d6 + 1d8+5+1d6 = 60.5
#2 Monk 11/Rogue 5/Warlock 4 same as above, but drop 2 skills with Expertise for an extra ASI, an extra Spell Known, and a Cantrip.
DPSR = 59
DPR = 60.5
#3 Monk 11/Rogue 4/Warlock 5 gets 4 ASIs, 2d6 SA dice, 4 skills with Expertise, no Uncanny Dodge, 3rd level Warlock spells, and another Invocation (can take One With Shadows to basically be a Way of the Shadow Monk while still going Way of the Open Hand). 1 less Sneak Attack die lowers our damage slightly.
DPSR = 52
DPR = 57
#4 Monk 12/Rogue 4/Warlock 4 Cross between #2 and #3 to end up with 5 ASIs! I don't think you need that many, but more feats can't hurt. You're MAD as it is, so a higher CON is a good thing.
DPSR = 52
DPR = 57
Or if we add Ranger in there (getting MAD, still assuming 20 DEX though, good luck with that):
#5 Monk 11/Rogue 3/Warlock 3/Ranger 3 gets only 2 ASIs...but that might be all you need to cap DEX. By RAW and the multiclass spell slot table, you only get 2 level 1 Ranger slots because you're considered multiclassed. The bonus here is Colossus Slayer and the Dueling Fighting style. Still using a Shortsword.
DPSR = 2d6+5+2+2d6+4d6 + 2d6+5+2+2d6+2d8 = 65
DPR = 1d6+5+2+1d6+2d6+1d8 + 1d6+5+2+1d6 + 1d8+5+1d6 + 1d8+5+1d6 = 65.5
Or if you insist that 6 Ki points (and therefore 6 Flurry of Blows) per short rest is enough:
#6 Monk 6/Rogue 7/Warlock 3/Ranger 4 has 3 ASIs, but puts out the highest numbers (as long as your Ki lasts). 3 ASIs is the minimum IMO, because you probably need 2 for DEX boosts and a 3rd for War Caster (important for maintaining concentration on Hex). Took Ranger to 4 instead of Rogue to 8, because it gives you an extra spell slot (which oddly enough, Warlock 4 won't give you).
DPSR: 2d6+5+2+2d6+8d6 + 2d6+5+2+2d6+2d8 = 79
DPR: 1d6+5+2+1d6+4d6+1d8 + 1d6+5+2+1d6 + 1d6+5+1d6 + 1d6+5+1d6 = 70.5
#7 Monk 6/Rogue 6/Warlock 4/Ranger 4 for the same as above, but drop 1 Sneak Attack die for an extra ASI. A fair trade. CON or Resilient CON would be nice.
DPSR: 2d6+5+2+2d6+6d6 + 2d6+5+2+2d6+2d8 = 72
DPR: 1d6+5+2+1d6+3d6+1d8 + 1d6+5+2+1d6 + 1d6+5+1d6 + 1d6+5+1d6 = 67
#8 Monk 8/Rogue 6/Warlock 3/Ranger 3 is the same as above, but you drop 1 ASI and a Ranger spell slot for 2 more Ki. As stupid as this sounds, this might be the best compromise. You still have 3 ASIs to cap DEX and grab a feat like War Caster for maintaining Hex.
DPSR: 2d6+5+2+2d6+6d6 + 2d6+5+2+2d6+2d8 = 72
DPR: 1d6+5+2+1d6+3d6+1d8 + 1d6+5+2+1d6 + 1d6+5+1d6 + 1d6+5+1d6 = 67
tl;dr Build DoT, not burst. Throwing Ranger 3 in boosts damage a bit. 6 Monk > 11 Monk, but you have to Short Rest as much as possible. 8 Monk is a possible compromise. Builds #6, 7, and 8 are best, depending on how many Short Rests your group takes as well as how many ASIs you want/need.