The short answer is No, they are not vegan-friendly.
ASDA’s Cola Flavour Bottles 50g are not vegan or vegetarian. This is because the product contains beef gelatine, which is derived from the hides and bones of pigs, cows and other animals.

Here are the ingredients according to ASDA’s website: Glucose Syrup, Sugar, Beef Gelatine, Acidity Regulator (Citric Acid), Colour (Plain Caramel), Flavouring, Coconut Oil, Glazing Agent (Carnauba Wax)