This sounds like a typical case of trauma and the treatment won't be easy.
You must remember that dogs are less intelligent than humans. They think in simple categories like "good" and "bad". Getting food, playing and cuddling is good, fear and the smell of smoke or fire is bad.
When the smoke alarm went off back then, your dog experienced the smell of smoke (which triggers a natural flight instinct) and your fear / panic in combination with the loud noise. This is a traumatic experience and very bad.
What happens now?
Your dog has forgotten the initial event that caused his fear by now. But he has not forgotten the connection "loud beeping noise = very bad". Your behavior during the last years has reinforced this connection to "any beeping = very bad".
A reoccuring error is that you think you do your dog good by allowing him to leave the house when he's afraid, but what you actually do is confirm that your dog has a valid reason to be afraid and reinforce his behavior.
How to treat?
First of all, you must treat the trigger (beeping noise) as the most normal thing in the world. Yes, there was a beep, but it doesn't scare you, you haven't even registered it. Don't look at your dog as if to tell him "Did you hear that, too?". No, nothing's happening, everything normal, carrying on.
Then you should desensitize your dog. Because the fear has been reinforced over years, some approaches might not work for your dog and you have to try something different. Unfortunately, describing every step and variation in detail would be too much for the scope of this site.
Please research the topic online or use the services of a professional dog trainer. Since your dog is triggered by a sound, you can find instructions with the search terms "desensitize dog fireworks" or "desensitize dog loud noises". Video tutorials tend to be better for learning because you see a dog reacting to the training rather than reading information alone.
What desensitization does in general is either teaching the dog that the trigger doesn't precede any bad consequences (thereby removing the mental connection "beeping = very bad") or - even better - teaching the dog that the trigger precedes positive consequences (thereby overwriting the trigger with "beeping = good").