It's not uncommon for double breasted jackets and coats to have their buttons moved, to fit the wearer. If you line up the side seams, you can see where the buttons were originally - If the button holes are in the centre, then it was originally a single breasted coat that was adapted for a smaller wearer. If the buttons are off on one side, then it's double breasted - and you can see where the buttons were originally. Sometimes buttons are quite close to pockets on double breasted styles though, so that alone is not cause for concern.
I agree with others that your coat is probably '60s, made of cotton velvet and perhaps rayon or acetate lining. I'm not sure what you mean by '20s pockets? They look like pockets with flaps to me, popular in many eras, indeed they never really go out of fashion.
When dating a classic style like this, I look to fabric, construction, detailing and labels for the best information. Eg, when you say the buttons are "shell", do you mean mother of pearl? Can you tell if they've been machine made or hand carved? How are the button holes made? I would expect an older garment of this sort and fabric to have bound button holes, but they look machined. Is there any shaping at all in the body? How is the inside secured, eg, are there buttons to secure the flap of the double breasted panel or a tie? How is the hem sewn? Machine, hand, with heming tape, secured to the lining? All of these give clues to the dating.