So you have mastered the spear...
So what I'd like to know is if there are any mechanics, feats, or class features that I am missing to make such a build possible
Yes. Ki-Fueled Attack, an optional monk feature from Tasha's Cauldron of Everything. If you can find ways to use Ki points as part of your Action, you can use an unarmed strike or monk weapon to attack as a bonus action. Not dual wield, but attack.
This is typically used to make extra attacks with weapons wielded in two hands, like longswords (katanas) or longbows (or muskets), that become monk weapons as part of the Kensei's ability or as part of the Dedicated Weapon optional feature (also from TCoE).
There is potentially some kind of synergy with Dual Wielder adding +1 to AC while holding two weapons, on top of Kensei adding +2 to AC if you attack with unarmed strike while holding a kensei weapon. With utter focus on wis and dex, you could get a reasonable AC, although only reasonable - armour + shield outpaces you at lower levels, and wizards et al ability to escape from melee attacks in various ways outpaces you at higher ones.
if this would be too unbalanced for a DM to consider accepting the weapon to be used with Martial Arts of Flurry of Blows?
No. There is no particularly powerful combinations allowed by using a weapon instead of unarmed strike for martial arts and flurry of blows. A few builds do use monk-with-weapon, but usually they rely for their power on other elements of the build and the bonus action attack from monk is an afterthought that could be added in other ways.
A DM not allowing this for balance reasons is misreading the math of the ability.
...but have you mastered it well enough?
RAW, your options are fairly limited. The big draw of Kensei is usually taking a 2h weapon to maximize the fairly limited potential of weapon attack, unarmed strike, weapon attack (as bonus action) after using Ki for Deft Strike, Stunning Strike or Focused Aim.
With two weapons, what you are mostly getting is +1 AC from the dual wielder on top of Kensei's +2. To get that you need a feat, to spend one of your attacks not using your weapons and then your bonus action attack (offhand) loses dex to damage any turn you don't spend Ki on your main attacks. This can be fine in a fairly non optimized game if you go Variant Human for the free feat and you're using point buy (so +1 on top of 15 gets you 16, and +2 from another race would get you 17 - same modifier). But 5e games tend to be optimized due to the fairly simple math and obvious optimization routes included in the game - you rarely see a character without a maxed out fight stat from character creation.
It's simply the case that outside of some fairly considerable cheese, dual wielding just sucks. It's sucked for like 4 editions of D&D at this point. Monk having built in extra attacks from early can be used for some stuff like Hexblade dip to add damage to all those attacks, but two weapon fighting just overlaps too heavily with what they can already do - the few builds that make use of Kensei are usually using it to bypass two weapon fighting limitations with a 2h weapon, usually a 2h ranged weapon (for Sharpshooter) so it doesn't add a lot to what you're doing if you're already using two regular one handed weapons anyway.
Essentially, and especially if your GM is a stickler for RAW/not even reflavouring stuff, you will do better as a Fighter or a Barbarian than a Monk if you want to use two spears or batons. Monk gives more flavour with deflect arrows and slow fall and stuff though, so you might choose that for that reason, but damage and survivability wise you will be lagging behind even other monks, which is saying something.
