Epic Guide to Baileys Irish Cream Liqueur ... there is no gluten or wheat listed as an ingredient. The official website says ...

1.5 oz. aged rum 1.5 oz. coffee liqueur ~2 oz. h eavy cream, semi-whipped so its thicker but still pourable Combine rum and liqueur in a mixing glass with ice and stir 15 to 20 seconds until chilled.