This is an old red and black paddling jacket and it appears that the black has lost a lot of the water proofing layer (the red seems fine).
Is there a way to re-proof this?
Yes, you will find spray cans to re-waterproof garments in general stores. Works well for windbreakers, ski gear, shoes, tents, backpacks, umbrellas...
Things like www.amazon.com/Scotchgard-Outdoor-Water-Shield-10-5-Ounce/dp/B004ZP83H8