Can I replace baking soda with bread flour in a cake recipe that already has baking powder?

No. Not at all.

Baking soda is a leavening agent. Together with baking powder it gives your cake lift and airiness. Bread flour is just flour with a higher protein content. If anything, it will make your cake more dense (though not in such small quantities as you would have for baking soda). If a recipe calls for both baking soda and baking powder, the recipe is balanced to rely on both and omitting one will cause the recipe to fail (to some degree). How it will fail will depend on the recipe, which you haven't included.

If you already have baking powder, and don't have the time to find baking soda, I recommend that you instead find a different cake recipe that uses ingredients you already have at home - specifically one that does not require baking soda at all. Many cake recipes use only baking powder, so this should not be overly difficult.

You may be able to replace the baking soda with baking powder at a powder to soda ratio of something between 2-1 and 4-1 depending on who you ask (e.g. two teaspoons of baking powder for one teaspoon of baking soda). Depending on the type of cake this may create off flavors in your final product. This and other possible substitutions for baking soda in cakes are discussed on this site in the related question: Replacements for baking soda in a cake?

Note, while these options are available to you, I still recommend finding a different recipe, particularly if you're not set on this specific one you're already using.

Also, since you mention bread flour, I hope you're not using bread flour for your cake instead of all purpose flour or cake flour. These three flours are quite different and will cause different outcomes if you use one when the recipe calls for another.

No, baking soda and flour serve different purposes in a cake. Baking soda is a leavener: it makes the cake rise. Flour gives the cake structure.

The way baking soda works is that it is a base, and when it reacts with an acid, it creates air bubbles which cause rising. Baking powder, on the other hand, contains both acid and base, and creates bubbles when it gets wet.

Likely, the recipe calls for both baking powder and baking soda because there is another acidic ingredient (such as lemon juice, buttermilk, or dark brown sugar) to balance the acid-base ratio. You may be able to reduce the acidic ingredient, remove the baking soda, and add a little more baking powder - but I can't say for certain without reading the whole recipe.

No, this is not possible. Flour and baking soda in cake, each with its own usage. If you want to use another substance instead of baking soda, you should use baking powder. Of course this is not always possible. Only in some cases you can replace baking powder, which Recipe does not contain acidic ingredient(Or contain small amounts of acid such as lemon juice). Because baking powder also contains acid. And no other acid is needed to react. source

If the recipe specified both baking soda and baking powder because it was ignorantly written, or written with a hidden agenda (make it more reliable because many people overstore baking powder but at least one of the leaveners will work), yes.

If the added baking soda is there because the recipe also has a surplus of an acidic ingredient, it might work fine enough if you replace the baking soda with more baking powder, but your result will be slightly more acidic, which could aslso influence subtler effects of recipe chemistry, eg sugar inversion or caramelization.