I’ve not used Delightful Reading, so this post isn’t about the program. Learning to read does involve both sounding out, and at some point memorizing words. For average children, this is fine, and will work to get them reading well. For some kids, memorizing can mask the fact that they don’t have good phonetic skills, and they may need more intensive phonics.
This is especially true of dyslexic kids. We are just starting down the path of learning about dyslexia in our family. Its a weird, catchall diagnosis, but the truth of it is that some kids develop lots of coping mechanisms (like memorizing) that can obscure the fact that can’t sound out unfamiliar words.
As for AAS, you aren’t supposed to start spelling instruction until the child is reading well, (per their website) so I’d stop that for now. You *might* need a different program, but it will just depend on your child. Keep hitting the phonics, and see if he can catch on with that.