Sounds ok - the six layers of flannelette make me think it'd be pretty bulky for not much absorbency, but other materials would be more expensive, so I guess its a good compromise. Sounds that these are to go directly onto baby's skin though (as opposed to stuffing for a pocket)? Personally, I'd just as soon go for the microfibre if its just going to be stuffed into a pocket. As long as the microfibre doesn't touch skin, I reckon it gives you the best of both worlds - more absorbent than cotton, slim-fitting and quick drying. Just fold a couple into thirds and stuff the pocket. Brill.
As for liners, we have eenees flushables at home but I rarely remember to use them. (They are good when I actually remember, lol.) But they are useless for newborn poo. It just seeps straight through them. Same with the J&J ones. I wouldn't bother buying those - I'd just go for a sheet of microfleece and cut strips to make your own liners. Microfleece will feel nice against baby's skin, does a better job of protecting the nappy and rinses out easily.
Just my two cents there.
ETA: re the pockets being a good, less complicated nappy compromise, I totally agree. I know that when I'm leaving Natty with a babysitter (and DH) that if she has plenty of pockets to wear, then they are just as easy as sposies. Though, I do find people cringe at the poo factor, but I tell them to just leave it for me to deal with. I don't care.