No.
Most rescue centres would visit your home and ask about your working hours so you wouldn't be allowed to re-home anyway. They would class your situation as unsuitable.
There are other reasons:
Vets bills are extortionate. Yes you can get insurance but this is tricky and some pet owners have been left with huge bills anyway because the insurance have wriggled out of paying. There is much more they don't cover than stuff they do.
The added expense of dog food and kennelling fees. Trust me, people may say they will look after it when you are away but most people soon tire of this. Not many are willing to walk a dog in the rain, pick up its poo and have their house smelling of damp dog. All those people who have said yes will suddenly find themselves busy so don't make the mistake of thinking that there will always be someone to look after the dog. Instead go on the assumption that most people will say no.
Dogs smell. There is no getting away from it. My neighbour got a dog not long ago, just a puppy and now her house smells of dog food and damp dog. You might get used to it but everyone who visits will know you have a dog before they even see it.
Your ds will get bitten. He just will. I know dog owners love to think their pets are gentle natured creatures from the planet 'Fluffy' but dogs communicate through tail wagging, barks and bites. You would need to get a dog that is used to children and being around children which would rule out most rescue dogs.
You would need to walk it at least twice a day, every day come rain or shine. Even if you are ill, the dog will need to go out. If you don't let the dog out (and since you have no garden you can't do it the easy way) the dog will piss and shit in your flat.
The noise. If you are out most of the day the dog may well bark and neighbours will complain. You don't know if a dog has this problem until you get it and start getting complaints. People who live in flats are not very tolerant to noises and you will be reported to the RSPCA by someone who is fed up of hearing the dog bark and is concerned about it being cooped up in a flat all day.
Dogs are animals that need love and care. They are not just companions for you. They are not creatures that are meant to be kept indoors for long periods of time. They need to have plenty of exercise, they need the fresh air, they need lots of time and attention, they need a good balanced diet, etc. Unless you can give all of that then I'm afraid you should reconsider.
Right now, the fact that you live in a flat, that you have a young son and that you work outside of the home for long periods all mean that you shouldn't really be considering having a dog.
If the rescue centre won't consider re-homing a dog with you then you shouldn't be considering getting one.
I can't believe other dog owners are encouraging you. They should know better. It's a classic case of putting your own needs before that of the animal. Yes everyone does it to a certain extent but in your case, it would border on cruelty. No dog should be kept in a flat no matter how small the dog. If you don't have the facilities to keep pets then just accept that you can't keep them.