Is there a reason why you think your son needs a pillow?
I started giving a pillow to my son since he was 16 months old, now he's 19 months and a bit. It's a very flat pillow and my motive at that time was to give him something that he can attach to when he goes to sleep on his own - Yes, he only started to sleep on his own at 16 months old But I checked on him from time to time and just never found him sleeping properly on his pillow. He's either hugging it or the pillow's tugged under his tummy!
I believe that's what gonna happen to your baby too !!!