I think you could say "i dream of" when you are talking about a wish or desire, and "I dream about" when you are telling someone about dreams that you have regularly. for example "I dream of swimming with dolphins" - i wish i could do this in the future "I dream about flying nearly every night" - i go to sleep and dream I can fly.

I created a video that answers this question. You can see it here: https://youtu.be/4YCow4Ya0uo

As Kevin says, they are very similar. Both "of" and "about" are prepositions, and many prepositions have very subtle shades of meaning. I was trying to think, anecdotally, how I may use them differently, but it was hard. For every rule I "invented", I realized that I could use the words interchangeably.

I think they are close in meaning. Dream of may be somewhat more specific than dream about. But I looked on line a bit and don't see any good distinction between these terms. If there is, it is very subtle.