(I was just going to comment, but the comment got larger and larger...)
OOh, screams? That would take a lot of dampening. I'm no expert on the matter, just what I've been taught added with logical thinking, but it seems like you would need a very thick, very heavy enclosure. There's no substitute for mass. I don't think you can have a mobile dampening booth, not a very effective one anyway. Especially if you're gona be screaming your guts out.
I suppose it depends on the type of scream too though; a high-pitched scream would be easier to dampen than a bassy one. I suppose it also depends on how much you want to dampen it too.
If two of the walls are solid outside walls, you could put the booth in the corner, so you have two less sides to build and move around. You could also cover any windows with extra dampers, maybe permanent.
Things like hinges mean there would be gaps, which impedes the effectiveness of the booth to quite a degree. You would need to resolve this somehow(e.g thick rubber or something). Sound will escape through any gaps or weak points, making the booth less effective. It's like a chain is only as strong as it's weakest link.
Why the air gap? I haven't looked into this for a while, but I don't think air gaps would make a difference. I can't see how it would help to take energy out of the soundwave. If anything it would just divide up the mass. But I'm not 100% on that.
You could try it though if you have the time, the reddies and the desire. You could measure the sound level in a certain place before and after construction if you are able. Then take measurements whenever you make additional changes to check the impact it has. Ideally, the sound source for testing would have a consistent level, so not a live vocal, but maybe a recorded one.
Maybe instead of building a booth, you could hire a more suitable space for an hour or two a week. Years ago, when I was living with my parents, I used to hire the local community centre for a few hours to practice DJing at a descent level. I did this once a week and it cost me £10 each time. Not bad considering I could go nuts there and not bother anybody. Just another angle to consider.