Hi,
The flags translation interface can only work with Falang.
If you don't want to use Falang, then you need to duplicate your products (once per language), duplicate your categories (once per language) and duplicate the menu items and modules of your shop.
That way, you can assign the menu items and modules based on the language and use their "main category" to select their main category of the language selected in them.
It's a lot of duplication, which is not required with Falang, but if you don't plan on changing often your products / categories, and you don't need to manage the stock of your products, then it's not a problem.
In other cases, it's better to use Falang to translate your shop content.