I'm shocked you would even ask the question! Of course they can.
Willow Brown, one of the main characters of
An Ordinary Fairy (she's the ordinary fairy, BTW), is a highly skilled
flier, in fact, one of the best in the fairy world. Perhaps a few words on the different types of fairies would be appropriate.
First, fairies have insect wings, not bird wings with feathers. They are classified into sub-species based on their wing type. (BTW, fairies are the almost the same species as humans -
homo aviatus. And they can
successfully cross breed with us, though the results are interesting.) All fairies wings are attached somewhat differently than on the
corresponding insect, allowing them to pivot downward, which allows ease of movement in tight spaces and concealment under clothing. The wings are supported and moved by a large structure of muscle, bone and cartilage on the upper back. Hence, fairy women don't wear low-back clothing. Fairy men don't have that problem, since they don't have wings at all.
The largest group is the Butters, who have butterfly wings. Many people consider them the most beautiful of all fairies. They tend to be a little stuck on themselves and perhaps a little slow-thinking, but as my information comes from Willow Brown, it may be slanted. They don't fly very fast, and tend toward jerky movements in the air. A related group is the Moths, who for obvious reasons, live on third shift and only come out after dark.
The next group is the Bumbles, who have small, black-veined bumblebee wings. They fly very little, due to their tendency to be, shall we say, portly. Many of them become healers and mid-wives. Because of their body size, they blend in well with humans, and many take on regular professions.
The smallest group is the Wasps. They are tall, thin-
limbed and have long wings. They tend to be very territorial and can have unpleasant
dispositions. They fly very well, though not as well as the last group.
Last, comprising about twenty percent of all fairies, is the Dragons. Willow Brown is a Dragon, with two pairs of dragonfly wings. Dragons are by far the fastest and most agile
flyers, able to perform wonderful
in-flight acrobatics. Some are better than others, just as some of us humans are better athletes. All fairies are very muscular and solidly built, in order to
accommodate flying. How does flying work? I'll quote Willow's explanation to Noah: "It's sort of a combination of physics and magic."
Just ask Tinkerbell.