Well, and I may be missing something, grappling a creature doesn't deny it's dexterity bonus nor does it qualify you for flanking.
Grappled: A grappled creature is restrained by a creature, trap, or effect. Grappled creatures cannot move and take a –4 penalty to Dexterity. A grappled creature takes a –2 penalty on all attack rolls and combat maneuver checks, except those made to grapple or escape a grapple. In addition, grappled creatures can take no action that requires two hands to perform. A grappled character who attempts to cast a spell or use a spell-like ability must make a concentration check (DC 10 + grappler's CMB + spell level), or lose the spell. Grappled creatures cannot make attacks of opportunity.
The grappled condition only applies a dexterity penalty, not a complete denial. So grappling alone will not allow you to sneak attack an enemy.
Edit: Missed the strangler feat, disregard me.
It is a little hard to tell how many levels of each class you're taking though. It looks as though you're taking 17 vivisectionist 3 monk?
The one thing I can think of is by mid levels you'll start to run into freedom of movement, and that will completely shut you down.
Also, you should look at what your CMB is versus opponents of the same and higher CR to know what your likelihood of successfully grappling is.
It looks like he's focusing on using unarmed strikes anyways, so he doesn't really need the extra arms in the first place. They don't grant additional attacks.
Also, watch out with knock out artist. It does require you to have an opponent denied their dexterity to function. So it will require you to pin your opponent for it to be used.
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Bruno opinion:
Drop Vicious Stomp & Improved Trip. Pick up Turtle Style and Turtle Clutch to improve Grappling economy. Pick up Greater Grapple at L9--again, improving action economy. Your sneak attack damage is contingent on the pinned condition, so you need to get there quicker.
First three levels: Monk with Maneuver Master/Weapon Adept archetype
Rest: Alchemist with Vivesectionist archetype
1: Feat: Combat Reflexes
1: Human Feat: Snapping Turtle Style
1: Monk Feat: Improved Unarmed Combat
1: Monk Feat: Improved Grapple
1: Monk Ability: Flurry of Maneuvers
1: Monk Ability: Perfect Strike
Weapon Adept's Perfect Strike will help you with those "must land grapples" and offset flurry of maneuvers penalty if you grapple as part of FoM
2: Monk Feat: Dodge
2: Monk Ability: Weapon Focus-Grapple
Dodge to boost AC/synergise with Turtle Clutch--why waste feats on trip if you're gonna grapple something. Either you invest in grapple or trip, so better to be good at one than mediocre at both (especially since you want Sap feats too). Weapon focus to boost your CMB on the Grapple.
3: Feat: Snapping Turtle Clutch
3: Monk Ability: Fast Movement
3: Monk Ability: Maneuver Training
3: Monk Ability: Maneuver Defense
At this point, if someone misses you while in Turtle style, you get an immediate action grapple, then on your next turn you pin them. Now, add alchemist levels.
4: Alchemist Ability: Brew Potion
4: Alchemist Feat: Throw Anything
4: Sneak Attack: 1d6
5: Feat: Strangler
5: Alchemist Discovery: Chameleon
5: Alchemist Ability: Poison Use
6: Alchemist Ability: Swift Alchemy
6: Sneak Attack: 2d6
7: Feat: Sap Adept
7: Alchemist Discovery: Lingering Spirit
8: Sneak Attack: 3d6
9: Feat: Greater Grapple
9: Alchemist Discovery: Bleeding Attack (Rogue Talent)
Ok, so, this is an Ideal Series of Events:
-Enemy attacks you. They miss.
-Turtle clutch triggers, you grapple them as an immediate action and give them grappled condition.
-Your turn. Move action greater grapple them to pinned status. You standard action grapple to do non-lethal damage for 1d6 (Unarmed) + STR + 3d6 (Sneak) + 6 (Sap Adept) + 3 Bleed (Bleeding attack). (No Strangler because of immediate action.)
-Opponent fails to break grapple.
-Move action Greater Grapple to do non-lethal damage for 1d6 (Unarmed) + STR + 3d6 (Sneak) + 6 (Sap Adept) + 3 Bleed (Bleeding attack). Swift action to add Strangler for another 3d6 + 6 (Sap Adept). Standard action to do non-lethal damage for 1d6 (Unarmed) + STR + 3d6 (Sneak) + 6 (Sap Adept). Full round damage: 2d6 (unarmed) + (2xSTR) + 9d6 (Sneak) + 18 (Sap Adept) + 3 Bleed. Or 59.5+(2xSTR) Avg DPR if the opponent is vulnerable to non-lethal AND precision damage.
In Bruno opinion, too many cons to this build:
1) Assuming you make some serious investments in your STR and your Grapple CMB, you'll be somewhere in the low/mid 20s. Against humanoids you will be fine, but against larger creatures you'll probably be 50/50 to land a grapple.
2) Until L9, your DPR is gimped because you can only do one grapple check per round until you bring Greater Grapple online. Not only that, your damage is contingent on being non-lethal and precision.
3) I forgot to write the CMD down for the above build, but you may have problems holding a creature if it tries to break the grapple.
4) This is a very MAD build: STR for Grapple CMB, DEX for AC, INT for Alch and CON because monsters are going to skip breaking a grapple and full attack you (or you miss a grapple and they full attack you). You can dump CHA and that is about it.
5) You have no ability to suppress or deal with liberating command or freedom of movement or teleporty stuff. You can't depend on a party caster spending their action to cast a spell just for your schtick or that they'll beat the dispel DC.
While flavorful, Bruno suspect you get frustrated by lack of grappling action economy, vulnerability dependencies and MADness...especially if you play this from L1.
Grappling can be pretty cool when it works, but its also highly situational. For one thing, you'd want some way of getting Enlarged. As you go up in levels, you'll be fighting more and more large and larger foes and that is going to make it that much harder to even land the grapple in the first place, much less maintain it. I tend to agree with Bruno that this might work if you play the build for a few sessions, but if you are playing him from level 1 on up, I think it will get frustrating. On the flip side though, grappling is easiest at low levels, so maybe take enough ranks in Maneuver Master to get to Greater Grapple ASAP.
If you are going to be playing from level 1, I would definitely recommend being prepared to be able to help out in additional ways other than just through Grappling.