My parent born in HK,I born New york n under 18 years,Can I apply HK ID Card at China consulate,NY.

It is hard to say whether you have the qualification for apply a HK card. You can refer to http://www.gov.hk/en/residents/education/preprimary/ to find the related regulations to make sure that you can apply or not.
If you have the qualification, you can apply for this card at China Consulate, NY.
Hope this information can help you.