My rubber boots are cracking where they form folds when I walk, as well as the soles attachment. What is a generic name of a flexible and waterproof substance/product that I can use to patch/glue? I know that specific product/brand recommendations are discouraged, but I'd like to know what type of ingredients work. eg is rubber cement flexible enough? Do silicone-based glues work for this?
For a specific product, I recommend Shoe Goo. It is designed for repairing shoes, in my experience it does work rather well. It is good for sticking them back together, and reattaching the soles if they have separated. Though maybe not so effective for repairing cracks where they are splitting.
I'm not sure if there is a generic term for Shoe Goo - according to Wikipedia, it is composed of "toluene, styrene-butadiene copolymer, and solvent naphtha". So you may be able to find something similar.
Also its probably a bit late for your boots, but rubber boots may last long if looked after. Wash them occasionally, with mild soap and water, and dry them off. Then they can be treated with rubber conditioner. This will restore the shine of the rubber, and stop them from drying out and cracking.
Rubber boots are inexpensive for a reason. They do not last long. They are made to be disposable. Just go get another pair. There just is nothing that will glue your cracks together and stay together. I've used duct tape but forget about being waterproofed...just go get another pair. If you are worried about throwing them away, go punch more holes in the bottom, fill with soil and grow growies in them.