Plot

The One Night at Flumpty's Plot is the main plot for the One Night at Flumpty's series, and the origin of Flumpty Bumpty's violence, there are several theories about the plot and few is known about this, there some theories and evidences of the plot below.

The Beaver's Newspaper (Backstory)
Not much is known about the backstory, but however, the first evidence is the newspaper that the Beaver is reading, in it, we can see several texts with some evidences of the backstory, in this case, some of the Redman's origin, it says that Redman was a most likely red human that drunk lava and lives (kinda). The left bottom text says that the player should look the cameras. The left top text says that the worst nightmare is run out of toilet paper and shows a picture with a toilet paper, another detail is the plot of the first game that says that Flumpty Bumpty kidnapped the player, that are you, because he felt like it.

Flumpty's Plot Immunity and Death
In the Night 1, when the Office's phone rings and Flumpty calls, he will say that he is an egg. In addition, he explains that he is immune to the plot and according to him, he can transcend time and space, which means that he can travel through time and space. On August 31, 2015, Jonochrome released a canonical image to Twitter to follow up the cancellation of One Week at Flumpty's, confirming that Flumpty is no more and he will not be making any further Flumpty creations. Flumpty Bumpty died by having a great fall, similar to Humpty Dumpty, thereby losing his immunity to the plot and being unable to return.

The Owl and Eyesaur
It is unknown about the Owl's origin, through Eyesaur does. Eyesaur was created after Flumpty's "game unfortunate past contestants", The Owl most likely is an asian owl, then was placed on Flumpty's House of Horrors, the Owl's main actions most likely were hunt and eat, and later become a carnivorous animal.

Plot Results
The plot has so much confusions on it, so here is how it is supposed to:

In One Night at Flumpty's, The player, that are you, have been kidnapped by Flumpty Bumpty, because Flumpty needs a friend, but isn't the best at social skills, he wants you to play a "survival hide-and-seek game" with him and his friends. If you get a jumpscare, you lose the friendship game and die. But if you survive and make it to 6 AM, you become best friends with Flumpty.

In One Night at Flumpty's 2, Once again, Flumpty Bumpty and his pals have kidnapped you, a innocent civilian to play a "survival hide-and-seek game" with them. The rules of the game are simple: if you can survive until 6 AM, you and Flumpty become best friends. If Flumpty and his friends catch you, you will then "lose the game" and they will "rip you a brand new face". Flumpty and friends also have a set of rules to their game, and you must learn these as the night goes on. The only tool you have is a light switch, a computer with minimal battery life and two switches to close the vents (However, if you press the switch of an open vent, the vent that was originally closed will open up again because it has a string attached to both vent doors).

One Week at Flumpty's plot is still unknown and has few evidences and theories, in this case, Flumpty defeats Golden Flumpty, the only revealed thing is Flumpty's death, he lost his immunity to plot and he was unable to return again, being canonically, and that the player haved to kill his old best friend, but then he was killed along with his best friend by Flumpty, the two new friends of Flumpty, Champ and Chump, were introduced.

In addition, the two plots together and some of One Week at Flumpty's and the backstory:

One night in the town, New Dork, Flumpty presented a heartfelt speech about the importance of life. The stranger he was talking to didn't like his speech. He walked away, wondering why a talking egg was telling him about life. Flumpty got so mad. He shot the stranger with a gun. That was Flumpty's first taste of death. Out of insanity he ate an entire human baby, and that wasn't all. According to somebody, Flumpty killed approximately 100 billion birds with a meteorite that caused the apocalypse. Now, Flumpty is a character who has immunity to any plot and can travel through time and space, so he can do whatever he wants. Then Flumpty broke into somebody's house because he was cooking an egg. Flumpty was then voluntarily arrested for breaking and entering. He did this, just to escape the prison. Flumpty then got lonely, He found a empty place. He found it wasn't empty. It was full of other creatures, like Birthday Boy Blam, The Redman, Grunkfuss the Clown and the Beaver. These creatures had also done evil acts. "I couldn't be seen with them!" thought Flumpty. So he developed a disguise. It was a yellow, cracked variant of himself. But this made him develop a terrible alter-ego. The alter-ego's name was Golden Flumpty. Flumpty (not as Golden Flumpty) then kidnapped a person for fun to play a game. If he survived, Flumpty would let him go, If he didn't, his eyes got fried. Luckily the person escaped, Flumpty then decided to do it again. This time, with a better reward, if the person survived, he would become Flumpty's best friend. He also made two more friends, they were the Owl and Eyesaur, a fleshy monster that was made of the heads of Flumpty's game unfortunate contestants, but however, he lost the Beaver, who fell in the toilet and died. The same person got kidnapped again. But this time, for two nights. On the second night Flumpty declared that the person became Flumpty's new friend. "To become my best friend. You must kill your old best friend." Flumpty said. He declined to kill his old best friend. Flumpty then just upright killed him and his best friend, introducing Champ and Chump, years later, the Beaver finally returned, but this time as a mummy, Flumpty was tired of Golden Flumpty, so he defeated him, then, Flumpty died and lost his immunity to the plot and was unable to return.

Trivia

 * As summarized above, One Week at Flumpty's has the least theories and evidences than any other game in the series.
 * Not much is known about the Owl, Champ and Chump.