They're descended from dragons and have some dragonic elements such as the reptillian appearance, resistance to their element type and the ability to use a breath attack. But that is as far as it extends. There is no mention of them having dragon scales just as there's no mention of them having dragon wings.
Without dragon scales, there is no reason for them to have any bonus AC.
Could they be retconned into having dragon scales? Sure
Reading... parsing... understanding...
I never said Dragonborn don't have scales. I said they don't have HARD DRAGON SCALES.
Reading... parsing... sighing.