What age can my toddler/baby sleep with a blanket safely?  

6 months. The risk of SIDS greatly drops around six months. It is ok to sleep with a blanky at this time. I'd still stick with a flat, silky kind of blanket, nothing super fluffy. You can try tucking it in on the sides of the crib at his chest level.
6 month. At 6 months, a baby is out of the greatest risk for sids and can easily roll out from under a blnaket.
6 months. Generally speaking, a baby should be able to free themselves if their face gets covered or they get choked. For most babies this is around 6 months. The peak incidence for sids is 4 -16 weeks, so during that time it is especially important for your baby to sleep on their back with nothing extra in the crib. Even afterwards if the temperature is comfortable a blanket shouldn't be necessary.
Why???? Why does a baby ever need a blanket? If the room temperature is reasonable, the pajamas are warm, i see no need for a blanket. There are safer things to use for comfort.