I have looked at maintenance manuals, the Airbus website, and Wikipedia but still could not find a definite answer as to what trailing edge flaps the Airbus A380 uses.
Adding to @Bianfable's answer, I'd like to address the terminology/usage.
When referring to flaps on jetliners, single-slotted means single-slotted Fowler.
The way a slot is created is in one of two ways:
Fixed pivot point below the flap line (first image below)
- Slow airplanes
- Flaperons on jetliners
Flaps extend backward and down (Fowler)
- Main flaps on jetliners (e.g. A380)
Side note: A "compromise" between the two is using a deep pivot which creates large Fowler motion, and to then droop the spoilers to manage the big gap, as used by the A350 (see related Q&A).
For the first "simple" type:
[...] the lower cove panel has to be rotated upward with a slave linkage, so the simple flap turns out to be not quite that simple. The simple slotted flap is not used on any modern airliner as a main flap concept, but the concept is used for flaperons.[ref] [emphasis added]
The blue circle I added below shows that cove panel; it can be seen on the Boeing 777's flaperons (second image below).
Arrow showing the aforementioned door, also note the fixed pivot point. Source: Bill Abbott, CC BY-SA 2.0, via Wikimedia Commons
- Peter, K. C. "High-Lift systems on commercial subsonic airliners." NASA CR-4746, Sept (1996).
Further reading on developing the A380 high-lift system:
- Neittaanmäki, P., et al. "AERODYNAMIC DESIGN OF AIRBUS HIGH-LIFT WINGS IN A MULTIDISCIPLINARY ENVIRONMENT." (2004).