TL;DR: No sovereign national flag contains orange, green, and pink together. A search for “countries with orange, green, and pink flags” returns zero current national flags that meet all three colors.
The combination creates an empty result because pink is extremely rare in national flags. Countries pick colors with long heraldic and symbolic traditions, such as red, blue, green, black, white, and orange (or saffron). Pink rarely appears in official state palettes. That makes the three-way mix—orange, green, and pink—very unlikely in a single national design.
Technical and historical reasons reinforce this absence. Early dye and pigment limits meant bright, durable pinks were uncommon, so flags evolved without them. Vexillological practice also favors high-contrast, easily visible colors for flags at a distance, and pink often reads as a tint of red or is treated as nonstandard. Hue judgment is also subjective: some shades called “salmon” or “rose” may look pink to some viewers and red/orange to others. Close alternatives do exist: Ireland and Côte d’Ivoire use orange and green (with white), and India and Niger pair saffron (orange) with green—none include pink.
Related categories to explore are useful for anyone searching for “countries with orange, green, and pink flags.” Look at lists of countries with orange + green only, or at flags that include pink outside the national level—some municipal, regional, and historical flags use pink, as do many pride and cultural banners. For this query, consider browsing near-miss national flags (Ireland, Côte d’Ivoire, India, Niger) or collections of subnational and historical flags that use pink.