First off air does reflect light and can be seen if it is cooled to liquid form. The reason we cannot see the air around us is because of a lack of density not a lack of light reflection.
As for objects that do not reflect light, Surrey Nanosystems have fairly recently developed a material which reflects almost no light. This materials is called Vantablack and it absorbs 99.96% of all light therefore only reflects .04% of visible light. This does not render it invisible, but makes an object a featureless black void.
To achieve invisibility you don’t want to absorb light, but somehow allow it to either pass through an object without distortion or bend the light around the object so that it never interacts with the object. There have been some claims that the US, China and Russia have been developing technology in that direction to supplement or replace camouflage, but nothing of that nature has been seen outside of fiction yet.