Can I deduct learning disability cost of $3,600 per year for my grandson?

Not sure what you mean by "learning disability cost"----and you have not mentioned whether you claimed your grandson as a dependent on your own tax return.   If you cannot claim your grandson as a dependent on your tax return, it sounds like you provided a gift to help him--which is not deductible.

If he can be claimed as your dependent, then if the expenses you paid were medical expenses for a special program prescribed or recommended by a physician then you can enter them as such.

Maybe, but the child must be your dependent.

Special Education

You can include in medical expenses fees you pay on a doctor's recommendation for a child's tutoring by a teacher who is specially trained and qualified to work with children who have learning disabilities caused by mental or physical impairments, including nervous system disorders.

You can include in medical expenses the cost (tuition, meals, and lodging) of attending a school that furnishes special education to help a child to overcome learning disabilities. Overcoming the learning disabilities must be the primary reason for attending the school, and any ordinary education received must be incidental to the special education provided. Special education includes:

• Teaching Braille to a visually impaired person,

• Teaching lip reading to a hearing disabled person, or

• Giving remedial language training to correct a condition caused by a birth defect.

You can't include in medical expenses the cost of sending a child with behavioral problems to a school where the course of study and the disciplinary methods have a beneficial effect on the child's attitude if the availability of medical care in the school isn't a principal reason for sending the student there.

Only if he is your dependent. Even then, you may only deduct the portion of medical expenses that exceed 7-1/2% of Adjusted Gross Income (AGI) and then only as an itemized deduction.  Your net total itemized deduction would then have to exceed your standard deduction ($12,200 Single, $24,400 married, under age 65) before you saw any benefit. 

If he is not your dependent, the parents can take the deduction, under the theory that your paying the expenses is essentially a gift to them, so it was essentially them paying.