I can give a partial answer, here.

Oilcloth seems to be far older- at least, far more commonly used for something like rain gear , tents etc. An Old Master painting from , say, 1600 is essentially oil cloth: canvas that's been painted with linseed oil and pigment. The pigment fills the weave of the cloth, the linseed binds the pigment to the cloth and makes it water resistant. Linseed oil alone would make a more flexible cloth. The problem with linseed oil is that it polymerizes initially reasonably fast- a few days- but does not completely polymerize for years, as it slowly absorbs oxygen, and eventually becomes pretty hard. Practically speaking, there was a period in which oilcloth would tend to stick to itself and other things, when there was heat and humidity, and so had to be carefully hung up, dusted, not folded and stuffed away. Then there was a period in which it would be relatively free of that trouble- and after that, the oil would get hard and crack- just like the "craquelure" on those old paintings. So, though that's OK for something like a tablecloth, people would look for something better for raingear. Though sailors often would simply tar their canvas raingear, the iconic yellow color of fishermens' Sou' Wester hats and rain gear seems to have come in part from the yellowing of the linseed oil that made them waterproof.

Waxed cloth seems to have been around by the 18th c., but ( and here I can't be quite sure) mostly for smaller things, like wrapping packets of letters that have to get through an ocean voyage. I would speculate that , if rain gear was made from waxed cloth at this time, it was not common because the only practical wax available was beeswax. Beeswax would be somewhat expensive, compared to linseed oil, but it also has a rather low melting point. Anyone wearing a beeswaxed raincoat on a hot day might find wax soaking into their clothes- and that wax would be hard to wash out. When waxed raingear does appear in noticeable quantities, in the later 19th c., paraffin wax is available ( distillation of it started circa 1850)- which doesn't have the same problems.

William Henry Smyth:, The Sailor's Word-Book ( 1867)

Ralph Mayer: The Artist's Handbook