Kitchen roll is generally compostable, which means that it will break down reasonably quickly on a compost pile or bin.
It does depend on what the kitchen roll has been used for, as certain substances won’t break down in the compost. For example, you shouldn’t put kitchen roll in the compost if it has been used for oil spills or pet waste. A few small stains should be ok, as the kitchen roll will break down before it becomes a problem, but completely saturated roll should be placed in the general waste bin instead.
This is because oil is difficult for bacteria to digest, while pet waste and anything else harbouring unwanted bacteria or pathogens may attract pests to your compost heap or bin. If you’ve used your kitchen roll for ordinary food mess, it should be fine to compost.