james mcquilliam No I didn't read the other books I just read the five children on the western front and I understood it thoroughly.
Sarah No - toward the start of the story, Saunders recounts how the children last met the Psammead in "The Story of the Amulet," with one or two small details. It might help to know that in the same book, the children befriended a professor who went on one of their Psammead-induced travels with them (although he thought it was a dream); he re-appears in this novel as a secondary character. That's really all you need to know outside of the basic "Five Children and It" setup (children, Psammead, wishes). "The Phoenix and the Carpet" isn't even mentioned.
willaful You'll feel it a lot more if you do... though probably not as much as those of us who loved them as a child.