Hi peakoverload
Sorry, I didn't see your message before now.
Unusual-sounding material you have, I can't quite picture it but wonder whether it's some kind of impregnated cloth, like a drafting cloth perhaps. However being from India they could be something else entirely. If you are able to get a photo of them I would be interested in seeing it.
Meanwhile because of their size you are probably better off keeping them rolled up, as they will be easier to store that way. If you have copies made then you shouldn't have to access the originals too often. Ideally I would say to store them flat but this is only practical if you have a place to keep them, such as a big plan cabinet drawer.
I would recommend that you purchase some "acid free" tissue, lay it on the top of each one and then place a cardboard tube the width of the document or wider on top of that, at one end of the document. Roll gently around the tube. Keep the tubes in a good-quality storage container (either archival board - which I recommend - or polypropylene, which might be easier to get hold of).
If you can afford to get the documents conserved before you store them, this would be ideal The cracking would be stabilised so that no further cracking and potential losses of bits of the documents would occur.
I hope this information helps
Prue