Note that this article contains a lot of speculation. Do not take everything here as a fact.
Chicken Invaders 6 (subtitle has yet to be announced) will be the sixth chapter in the Chicken Invaders franchise, and will most likely release in a year from now in 2018.
Current development stage
It is possibly in the Alpha stage, in which InterAction Studios will be designing the plot, and making ideas. If you ask them, they can't respond, because "the universe you're trying to contact is out of reach". They currently aren't taking bigger suggestions, so the game is more likely to be in a later developement stage.
Until then, the holiday editions of Chicken Invaders 5 will be released instead.
Theories about the Plot
The Egg Cannon (with other bosses too) will come back in this Episode.
The plot might revolve around the Hero travelling through dimensions to stop the Chickens.
Currently, we know very little about this chapter, however you can speculate here.
- The Paradoxical Paradox was an Alpha name for CI5, but that was changed to Cluck of the Dark Side. Now CI6 is reffered as this. 
- They also put identical text within CI6 page. Maybe this name is only a joke, too...
- It is also possible that Paradoxical Paradox never happened, due to the nature of time paradoxes, that tend to cancel themselves out.