Some of the plants are quite recogniseable if you know the art conventions of the period. For instance, that plant in the illustration is pretty obviously Bryonia, with its long tendril, grape-like clusters of fruit, distinctively shaped leaves and weird hairy root with bulges. Bryonia was a poison, a medicine and a tool of magic, as well as a beautiful plant in its own right, and was often substituted for mandragora. The women-coming-out-of-tubes thing strongly suggests alchemy to me, since a lot of alchemical texts represented the process as a marriage or an act of ceremonial sexual congress. Check out the 'Book of Lambspring' or 'The Alchemical Marriage of Christian Rosenkreutz'.
What puzzles me more is that John Dee couldn't read it. He was a remarkable linguist and cryptographer.