Notes:

Titaani will move two squares forward, so she is in the square with the overturned table. She is going to throw her bucket's contents at the coal to the upper right of the bullywug, (the closest one to her).

Improvised ranged weapon attack: 12 Damage: 4

These things are very fast - the tiny coals hop and jump quickly and unexpectedly. Nevertheless, Titaani manages to douse one, nearly extinguishing it. (It continues to glow dimly, however.)

Cad is up next.  Ben and Titaani each have empty buckets, and a third empty bucket lay nearby. The coals dance angrily, while the bullywug races around in a panic. "Put them out! Put them out!"

Cadwallader:

Cad reaches in and grabs the empty bucket. On the way out of the hut he fires a ray of frost at the sizzling ember doused by Titaani. (15 for 2 cold damage)

He hands the bucket to Horatio.

With all the buckets in use Matilda gives it a go to kick the coals out the door or window and into the swamp.

Kick: Attack: 11 Damage: 1

BA Attack: 4 Damage: 1

Cad pushes past Matilda, grabs the empty bucket, and cleanly snuffs out the coal with his icy spell. It is now cold and inert.

The bullywug tries to whack the coal near him out the door toward what appears to be an exterior deck over the lake, with his spear:
Spear Attack vs animated coal: 22. Hit: 2 piercing damage.

He manages to hit it, knock it onto the deck, and even chip a piece off, but the coal remains dry and animated, if a little worse for wear.

The coals fight back, bouncing and skipping erratically.

Kindle Attack #5 vs. bullywug: 8 Hit: 1 fire damage, and the target catches fire.
Kindle Attack #4 vs. Titaani: 10 Hit: 2 fire damage, and the target catches fire.
Kindle Attack #3 vs. Titaani: 12 Hit: 3 fire damage, and the target catches fire.
Kindle Attack #2 vs. Cad: 17 Hit: 4 fire damage, and the target catches fire.
Kindle Attack #1 vs. Matilda: 19 Hit: 4 fire damage, and the target catches fire.

Matilda tries to kick the coal out the door, but the coal is much too fast for her.

Horatio is up next, then Titaani, Cad, and Ben.

Both the bullywug and Titaani are aflame. (Bullywug crit damage: 4) 
(Until they take an action to douse the fire, they will take 1d4 fire damage at the start of each of their turns.)

Horatio is up next, then Titaani, Cad, and Ben.

Horatio:

Taking the bucket from Cad, Horatio fills it with water then heads into the hut. He yells out, "Wrap your hands and just grab them, then dip them into the bucket. It'll be faster!"  (( I believe that is all I can do this turn. ))

Horatio is able to fill his bucket and get as far as the doorway.

- Top of the Round - 

Titaani, Cad, and Ben are up next.

Is Titaani still up? (She suffered 5 fire damage last turn, and takes another 1 fire damage at the beginning of this turn.)
The bullywug is also aflame.

Ben:

Filling the bucket by the simple expedient of jumping down into the water, Ben clambers back onto shore, sopping wet from head to toe and with a full pail of water.  He hands it to the nearest empty-handed person he can reach—or failing that holds it out for someone to take, saying, “Full pail here—someone grab it!”

Matilda grabs the pail from Ben and upends it on the nearest ember, then tries to kick it out the door again.

Kick: Attack: 21 Damage: 1

BA Bucket Attack: 5 Damage: 1

(Titaani has fallen down unconcious. :( )

Cadwallader:

Cad, seeing the last spell work, fires off another ray of frost at the nearest spark. (Disadvantage from being close: 7 for 1 cold)

Then he sees Titaani lying on the floor, her clothes still smoldering. He scoops her up and rushed out the door, calling for help.

((I assume Cad can carry her without any kind of check, given her small size, but let me know if I need to roll something. I think half movement would just get them through the door?))

Titaani collapses, her clothing alight with flames. (She will fail auto-fail one death save unless somebody takes an action to douse or smother the fire before the beginning of her next turn.)

Cad fires off a poorly-aimed magical beam before scooping up Titaani and retreating to the doorway.
Opportunity Kindle Attack vs. Cad: 21 Hit: 2 fire damage, and the target catches fire.

Ben fills his pail and rushes up the ramp with a full bucket of water to offer.

Shrieking with pain, the flaming bullywug races down the ramp to the south toward the foggy pond. (Additional fire damage: 3)

The dancing coals bounce around, setting fires:
Kindle Attack vs. Matilda: 24 Hit: 3 fire damage
Kindle Attack vs. Cad: 22 Hit: 4 fire damage
Kindle Attack vs. Cad: 25 Hit: 1 fire damage

Grabbing the bucket from Horatio, Matilda kicks at the coal and tries to douse it, but the coal is just ahead of her every move (17 doesn't quite hit!)

Horatio is up next!

You hear a distant splash and a sigh of relief as the bullywug has put out his flames by jumping in the lake off the deck.

Corrected Map (bucket placement):

Matilda gives up on the suprisingly dextrous embers and runs to smother the flames on Titaani...

Horatio:

Instead of running back and forth to get water, Horatio tries to use the bucket to smash the nearest ember. 

Bucket Attack: 16 Damage: 5

Running behind Cad and Titaani (unconscious and aflame) and circling around the closest coal, Horatio picks up the empty bucket that Titaani dropped and tries to smash the burning ember. But it's too quick for him, and he winds up denting the bottom of the pail on the charred wooden floor.

(Matilda's a little ahead of the curve - she already acted this turn. When it's your turn again you can decide if you want to keep or change your post. She's also on fire...🔥 )

--Top of the Round--

Initiative order:
Titaani  - unconcious, aflame
Cad - aflame
Ben - has full bucket
Bullywug - in the pond
Animated coals
Horatio - has empty bucket
Matilda - has empty bucket, aflame

Titaani may make one death save (and auto-fail another one.)
Cad and Ben may act next. Cad takes another 4 fire damage.