Aside from trippy 60's posters or album covers I don't really know much about Psychedelic and Visionary Art so I went on a quest to find some inspiring artists.
First, I learned there is a clear distinction between the two. Psychedelic Art seeks inspiration from hallucinations and Visionary Art from the meditative and spiritual. Both are only subtly different from Surrealist Art which gains inspiration from dreams.
Here are some contemporary art works that reflect the Visionary Art style.
There's actually an American Museum of Visionary Art that you can see here.