Nope! The 737-800 has eight emergency exits: four over the wings, plus two fwd exits and two aft. The fwd and aft exits use inflatable slides; only the overwing exits use the flaps as "slides." The aircraft most certainly does have escape slides.
Well duh! If you looked at the text that I had highlighted in the quoted section on my post it is clear that I was referring to the overwing exits and not the main cabin doors. I know full well how many exits there are on a 737 (all versions) and have worked on them numerous times as crew.