Wow, I had to google the palm houses, too. Aren't they just too impressive!
This thread just brings out the builder in me. I think you could get some of the shapes that you want with just about any material, but the problem is going to be the roof area. Most of us know it's pretty hard to grow edibles long term next to a window in the house. The bulk of the roof is going to have to be a material that lets light through. When you bring all those wonderful curves into the picture, you have a challenge. Plastic sheeting would work, but would be temporary. Harder plastic type sheets might fill the bill, but I don't have any experience as to how much bend they have. Curved glass would probably be cost prohibitive.
Some kids build a small greenhouse using cut plastic 1 liter bottles threaded on bamboo rods (or something similar), and actually it looked better than it sounds. Wish I still had the link, sorry. But that would be something that you could curve and might hold up fairly well.
Could you round the corners of your structure and not have glass there? Then for roofing, have a more typical, easy to build shape with a fancier facade on the front?
http://www.flyingconcrete.com has some great ideas for moveable forms for barrel vaults, but it's concrete. Might give you some ideas, though.
I think a lot of the folks on this forum don't have engineering and building skills of this magnitude to offer much advice on how to build that roof, but hopefully someone can help.