Flintlock is a term applied to a firearm that uses a flintlock mechanism—that's the Wikipedia definition and it's pretty boring and not very descriptive. The flintlock is an innovative tool in weapons technology, and it's fairly basic: create a spark (from flint and steel) that ignites the gunpowder in the barrel of the gun. It was invented in the 17th century and widely used for two centuries. It's the kind of gun used during the American Revolution or the Napoleonic Wars.
Flintlock Fantasy is set in an era where flintlock technology is used, but steam power is not—specifically, it may be Steampunk's cousin, but it is not Steampunk. What makes this sub-genre different from Gunpowder fantasy is the specificity of the gunpowder technology and that it tends to be influenced by history. Flintlock Fantasy is considered by some to be a sub-sub-genre of Gunpowder Fantasy, and others see the terms as interchangeable. The only real pitfall of using the terms interchangeably is that gunpowder was in use long before and long after flintlock technology, which creates a somewhat murky definition.
Flintlock Fantasy is a modern sub-genre of fantasy and it is still evolving and being defined. Flintlock Fantasy is different from other sub-genres in that it is not set in medieval times nor in the modern era of Urban Fantasies. It is fantasy that takes place at the cusp of industrialization, when warfare itself is changing. Thus, change and military might are common themes of the sub-genre. The tagline for Flintlock Fantasy would be: fantasy with guns.
Variable. While the sub-genre is named for a technology, magic is sometimes very much a part of the fantasy world and story. The detail with which the magic system is developed will vary from author to author, but what is really interesting about this sub-genre is how magic works with gunpowder. This pairing makes action scenes interesting and often contributes to the plot in some way. It's also an interesting evolution in fantasy because it shows how magic changes with the times and with technology.
As always, there are exceptions and some stories will use very little magic, and sometimes no magic at all.
Moderate-High. Flintlock Fantasy is a modern sub-genre of fantasy and it tends to have themes related to industrialization and revolution. There is usually questions surrounding the advancement of technology and its effects on society.
Moderate-High. Like other modern fantasy sub-genres characterization is important to story development. There isn't really anything specific to describe under this heading, other than the fact that soldier characters are quite common.
High. Flintlock Fantasy doesn't get as bogged down in world-building as other sub-genres (like Epic Fantasy) because it can draw on the reader's historical knowledge of the time period. World-building of course is still important as these are alternate world stories, but having this basis for the world means there's more room for plot development. There is room for different types of stories and plots in the sub-genre, but Flintlock does tend to more military inspired plots, with action packed scenes and epic battles, which often make for a more linear plot. This makes for a high momentum story, the plot is always marching forward. However, because the sub-genre is still evolving and being defined, it is difficult to characterize a typical plot.
Moderate-High. This is a sub-genre defined by the use of weapons technology—there will definitely be violence. The violence is militaristic in nature.
Gunpowder Fantasy. Flintlock and Gunpowder are very similar, so similar that the terms are often used interchangeably (also Muskets and Magic). Flintlock Fantasy is more specific and tends to be grounded in a historical period.
Epic Fantasy. Flintlock Fantasy is a sort of evolution of Epic Fantasy.
Historical Fantasy. Flintlock Fantasy in many ways is derived from Historical Fantasy, setting the story in a period where the technology is prevalent or just coming into usage.
Military Fantasy. Gunpowder being a weapon, there are obvious ties to military-focused stories. And flintlock changing the very nature of warfare makes a great crossover into the military sub-genre.
By Django Wexler. First book in The Shadow Campaigns series and a military fantasy.
By Brian McClellan. Trilogy where people called Powder Mages whose magical ability is manipulating gunpowder.
By D.B. Jackson. Heavier on the Historical Fantasy side, this series is set in pre-revolutionary Boston. Magic, crime, and history intermingle in a world on the cusp of war.
By Brent Weeks. Series where the magic system is based on color.
By Chris Evans. An empire is teetering on the edge of war in a world of muskets, cannons, bows, magic, and more.
By Brandon Sanderson. A spinoff of the Mistborn trilogy. The world is on the verge of modernity—railroads, electric lighting, the first skyscraper, and a new mix of magic and technology.
By Naomi Novik. This series is set during the epic events of the Napoleonic Wars, with the addition of dragons.
By Michael A. Stackpole. . In this first novel of the Crown Colonies series, the colonies are in turmoil. The story is complex with social, economic, political, military and philosophical interactions—with a good dose of magic.
By Susanna Clarke. Flintlock guns are not uncommon in this novel. It takes place in 19th century England when magic once existed and has returned, to two men. It is a novel about dualities, including the industrial revolution.
By Bradley P. Beaulieu. This series has a Russian/Eastern European style and tone and the addition of firearms lends a modern feel to an imaginative world.