Flux theme includes an option to have two product badges on a product card at the same time. 

You can also position them in different corners of a product image. 

One badge will dynamically show a sale badge if you set a discount for the product or a sold-out badge if the product is not available. For the sale badge, you can choose to show “discount percentage” instead of standard “sale” text by ticking the “Show discount percentage” checkbox in “Theme Settings->Badges”.

For the second badge, you need to use a product tag. For example, you want to show the “New” badge on the products you recently added to your store. You’d add a tag ( e.g. new ) in the product tag field of each of the products. Then in “Theme Settings->Badges” add the same tag in the “Custom badge tag” field. Now you can add the text for your badge in the “Custom Badge Text” field. Once set, every product that has that tag you set will now automatically display the badge.

You can also style your custom badge by using text and background color options.