Restored Dominican Republic
Who & why: the War of Restoration (1863–1865), a guerrilla-heavy popular uprising against Spain's re-annexation, ends with Spanish withdrawal in 1865 and the Dominican Republic restored for good. Rafael Trujillo's dictatorship (1930–1961) and every political upheaval since — the 1965 civil war and US intervention, the return to elected government — are changes of government, not of flag.
What it represents: the white-cross banner first raised in 1844 (see entry 4 below) becomes the permanent national flag from this restoration onward, with only minor refinements to the coat of arms and official proportions over the following century and a half — not separate flags, just one long, settled lineage.