Kleenex is the brand name of a type of facial tissue, the kind that you use for blowing your nose. It is an English name, but it is borrowed by French, and means exactly the same thing. "Des Kleenex" simply means, some Kleenex. (Technically, "des" means "of the" but in practice, "some" is a better translation.)
In French, "kleenex" is considered masculine, so it is used with the article "le." Therefore, you would say "le kleenex" when referring to it. However, keep in mind that "Kleenex" is a brand name, and in everyday language, people may also use the term generically to refer to tissues.
"des chaussures" are "shoes" in French.
"des pois" are "peas" in French.
"Des ciseaux" in French translates to "scissors" in English.
Des clés mean keys
des feutres are felt pens in French.
'des fleurs' means 'flowers' in French.
'mouchoir (en papier)' ou ... kleenex ! :-)
a Kleenex is called by its same brand name in French, or is called 'un mouchoir en papier'
'on a mangé des frites' means 'we ate French fries' in French.
des chaussettes are 'socks' in French.
The French "des Moines" translates literally to either "from the monks" or "of the monks".