Master Tamer Flummox

Roboteer:

This is a difficult battle as he has a combo of strong vs mechanical and a reduction to speed and attack.

Here is how I managed:

Sunreaver Micro-Sentry (2,1,1)
Lil' Bling (2,1,1)
Cogblade Raptor (2,2,1)

Start with Sunreaver: Extra plating, Fel immolate, Call lightning.
Switch to Cogblade Raptor: Exposed wounds
Switch to Lil' Bling: Inflation
Switch to Cogblade Raptor when Lil' Bling dies and finish him off with Batter.

You could possibly switch to Lil' Bling after Sunreaver and then to Cogblade - but this deviation hasn't been tested yet.

Hope this is a help :-)

The Lil' Necromancer - very fast and reliable 2 pet strategy:

Unborn Val'kyr (1,2,2)
Macabre Marionette (2,1,1)

Start with Unborn Val'kyr:
Curse of doom

Switch to Marionette:
Death and decay
Dead man's party

Marionette dies!
Switch back to Val'kyr:
Shadow slash until Flummox is utterly Flummoxed!

Hope this helps :-)

Flummoxed is randomly available in Suramar (25.20, 62.49) and only visible if you've unlocked World Quests.
Rewards will vary.

Master Tamer Flummox is a level 25 legendary with the following attacks: [pet-ability=1557], [pet-ability=1556], [pet-ability=111], passive buff: [pet-ability=956]

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• Tamer has two NPC pages (don't know why) where people are listing strategies in addition to the quest page. Quest, NPC1, NPC2.
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• Link to World Quest team/strat: here.
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• Originally at launch this tamer wasn't giving credit for Family Familiar - this has since been resolved.
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Master Tamer Flummox is part of Family Familiar
(Use the Spoiler tags to view the strats as they're developed/linked.)

Aquatic: Aquatic Acquiescence

• Team: [npc=71159] (2,2,2) | [npc=73359] (1,1,1) | [npc=70098] (1,1,1)
  Strategy: here | Credit: Purged

Gahz'rooki can be subbed with a (1,2,2) [npc=71017], but [npc=73359] & [npc=70098] have no alternates at this time.

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Beast: Best of the Beasts

• There seem to be a lot of variations for this fight with different combinations of spiders and pups:
  - If you have [npc=99527] (alts), [npc=93142], [npc=99526] (alts), use Randi's strategy (here).
  - If you have [npc=62864] (alts), [npc=72464], B/B [npc=62435] (alts), use Djongov's strategy (here).
  - If you have [npc=91823], [npc=93142], another beast, use TheManCalledZee's strategy (here).
  

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Critter: Mousing Around

• Option 1: [npc=64238] (1,2,2) (alts) + 2 critters with [pet-ability=165]
  Strategy: here | Credit: Chidsuey

This can be broadened to "a critter with [pet-ability=519]" and two "critters w/avoidance" - if not [pet-ability=165], then the [pet-ability=312]+[pet-ability=159] from a hare/rabbit/cottontail/bunny (list).

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Dragonkin: Dragons!

• Team: [npc=72463] (x,2,2) | [npc=9662] (2,2,x) (alt) | [npc=68662] (1,1,2)
  Strategy: here | Credit: kainwhisper

If you need help getting Yu'la from the Celestial Tournament, I had a lot of luck using mel9525's guide (here). Keep in mind you only need 12/15 tamers for the achievement, though.

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Elemental: Ragnaros, Watch and Learn

• Team: [npc=79039] (x,x,1) | [npc=73357] (2,x,2) | [npc=61703] (1,1,2) (only H/S and P/B are faster than Flummox, not sure if this matters)
  Strategy: here | Credit: Thatingles

Trying to find a middle pet to sub into ingles's strat that is more common, but so far no luck.

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Flying: Flock Together

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• Option 1: [npc=86716] (2,1,1) (alts) | [npc=86447] (1,1,1) | [npc=88452] (2,1,2) (alts-ish)
  Strategy: here | Credit: Lessiel
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• Two different versions with falcosaurs (orphaned hatchlings):
  - 3 falcosaurs with [pet-ability=518] & [pet-ability=1773] --- Strategy: here | Credit: Solacia
  - Snowfeather and Sharptalon Hatchlings (1,1,1 on both) + an owl with [pet-ability=184]+[pet-ability=256]+[pet-ability=517] (ex. [npc=97126]) --- Strategy: here | Credit: Xelians
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Humanoid: Murlocs, Harpies, and Wolvar, Oh My!

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• Team: [npc=90206] (1,1,1) | [npc=71014] (1,2,1) | 3rd Humanoid w/bigger attack, ex. [pet-ability=586]
  Strategy: here | Credit: Keepertje8

Looks like the breed of the Wolf can impact viability. See if the alternate moveset by briare (here) helps if you're having trouble.

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Magic: Master of Magic

• Team: [npc=71021] (1,1,1) | [npc=68658] (2,2,2) | [npc=71016] (?,2,?) (alternately: [npc=62317] (?,?,2))
  Strategy: here | Credit: Janathema

Strat is pretty straightforward, but commenters on OP have provided additional alts (like subbing [npc=68806] for Voidcaller).

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Mechanical: Roboteer

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• Option 1: [npc=68841] (2,1,1) | [npc=48609] (x,2,1) | [npc=88134] (1,1,1)
  Strategy: here | Credit: Avasam
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• Option 2: [npc=69778] (2,1,1) | [npc=73011] (2,1,1) | [npc=68841] (2,2,1)
  Strategy: here | Credit: Fedtmule
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Undead: The Lil' Necromancer

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• Option 1: [npc=71163] (1,2,2) | [npc=34770] (2,1,1) | 3rd Undead
  Strategy: here | Credit: Fedtmule
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• Option 2: [pet-ability=321] | [pet-ability=212] + [pet-ability=218] (list*) | Swarm ability ([pet-ability=1093] or [pet-ability=163] (list))
  Strategy: here | Credit: Ansawa
  *Ignore Unborn Valk on this list, spells share a slot.
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