Which term is more likely to have been used by my main character, a young man from a wealthy Macon, Georgia family, in 1893?
According to Hans Kurath, A Word Geography of the Eastern United States (1949), the local term for cakes made primarily of corn meal or primarily of wheat flour and cooked on a griddle or pan varied considerably across the South in the 1940s. There is no reason to suppose that the word preferences were more uniform across the entire geographical region 50 years earlier.
Unfortunately, this reference covers the Eastern Seaboard states only to the southern border of South Carolina, but it gives a strong sense of the variety of names used slightly to the north of Georgia in the 1940s, and (I think) invites some reasonable speculation about the likeliest candidates for Georgia in the 1890s.
Corn griddle cake options include johnny cake "which is current in several unconnected areas: (1) in the Carolinas, (2) in Maryland, southern Delaware, and the Northern Neck and Eastern Shore of Virginia, (3) in central West Virginia"; johnnikin "in the southern part of the Eastern Shore of Maryland and in coastal North Carolina"; hoe cake "in general use in the Carolinas and in all except the west-central part of Virginia, at least in folk speech or as an old-fashioned term"; corn dodger—a term "applied to a small corn cake (two or three in one pan)"—"in the South Midland (most of West Virginia, western Virginia, western North Carolina) and in the Northern Neck and the northern piedmont of Virginia"; and hobby "in West Virginia south of the Kanawha."
Wheat griddle cake options in the South include pancake:
and batter cake or batty-cake:
Various other regional terms for wheat-flour pancakes (griddle cake, fritter, hot-cake, and flannel cake (or flannen cake) are strictly or primarily Northern terms in the states along the Eastern Seaboard, according to this reference. (Flannel cake "has been carried southward [from Pennsylvania] into the Blue Ridge and along Chesapeake Bay.") Kurath doesn't mention flapjacks at all; I suspect that it's a Midwestern term; I remember as a child in the early 1960s seeing it used in a book of tall tales about Paul Bunyan and finding it extremely odd (I grew up in Texas at the other end of the South from Georgia).
It seems highly likely to me that griddle cakes served in Georgia in the 1890s—even in a well-to-do home—would have been made primarily with corn meal, and would have been called hoe cakes. If they were made with wheat flour, they might have been called batter cakes, but I think the likelier name would have been pancakes.
During that time frame in the South, hoecakes was the term. Field workers would literally use hoes as a makeshift griddle, and the cakes were made with cornmeal.
In the North, they called them Johnnycakes.
Native Americans cooked them on hot rocks.
A more traditional breakfast in the South would have been either fish and grits or else ham and grits, both served with biscuits in either case.
Considering that nobody used hotcakes before around 1900 (see Ngrams) I'd recommend flapjacks.
UPDATE: actually, they were spelled hot cakes then, and seem to have meant the entire class of foods consisting of griddle cakes, pancakes, waffles, and so on. See Google Books.
Use flapjacks for the book you are writing, the Georgians in 1890's might have used the same more likely, for their are many a books suggesting the same when speaking of that era.
The books and articles that used [Georgia as background] :
hotcakes [dated 1889-1900]
Note: Though hotcakes also pop out in the result but flapjack clearly outnumbers it.
Here are some more references suggesting use of flapjacks:
By the way it's a personal choice you have to make for both of the words existed and were used in that era.