"-desushi" mean "becase" and "and".
Let's take a look at a few quotes from episode 5 for example.
ふぉぉぉ！燃える展開です!! ちよりはバーニングチョリソーですしー!!
Wow! This is a burning development!! Because Chiyori is Burning Chorizo!!
るぅ子さんがやらないなら私がやります ちよりがやりたいですしー！
If Ruuko doesn't play, I'll play. Because Chiyori want to play!
The word "-desushi" itself is normal Japanese. But the overusing "-desushi" is part of slang of young people.
In this anime, "-desushi" is used for accent of character like "-nyo".