http://www.agriculture.purdue.edu/agcomm/ontarget/0603/Grammar_trap.htm
Grammar Trap: flier vs. flyer
When you meet a pilot, do you speak with a “flier” or a “flyer”?
When you put up a handbill, do you post a “flyer” or a “flier”?
Yes. And no.
Finding these words in the dictionary, you’ll see that “flyer” (aside from being a device used in textile production) is the alternate spelling for “flier.”
In other words, both spellings are acceptable, but as the dictionary definition indicates, “flier” is Number One and “flyer” is second banana. Some will try to tell you that one spelling is for pilots and the other is for handbills. Those people are wrong, and you shouldn’t listen to them. In fact, run from them. Fast.
Like any word that has different accepted spellings, it’s important to use one spelling to maintain consistency and avoid confusion. Most likely, these concerns are what prompted
The Associated Press Stylebook to affirm that “flier” is preferred for both aviators and handbills, while “flyer” is reserved for certain proper names such as Radio Flyer.
Of course, proper names are always written the way the owner wants them spelled (even if they are abominations such as “Kane’s Kandy Shoppe”).