Atypical fantasy but Naomi Novik's
His Majesty's Dragon might do it. The rest of the books in the series drift from the military aspect.
Quote:
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Aerial combat brings a thrilling new dimension to the Napoleonic Wars as valiant warriors ride mighty fighting dragons, bred for size or speed. When HMS Reliant captures a French frigate and seizes the precious cargo, an unhatched dragon egg, fate sweeps Captain Will Laurence from his seafaring life into an uncertain future – and an unexpected kinship with a most extraordinary creature.
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Promise of Blood by Brian McClellan is also sticking in my brain but I can't remember specific military things about it. Must be the mages with muskets
.