Can I install a garden chiminea in a wooden shed?
I love these garden fireplaces, but think you would be wise to keep it outdoors as it was designed for.  In my humble opinion, the fact that it is an open flaming device with flames viewable 360 degrees, it would be very dangerous to have it indoors. Sparks and embers could easily escape the enclosure with a draft from a door or window. As far a a flue is concerned, any flue passing through a combustible wall needs to be installed in a collar that insulates the hot chimney pipe from the walls, or a special double or triple wall insulated pipe and collar should be used.  Looking at your pic, it appears the chimney is tapered for cosmetic appeal. This type of pipe may not match up with standard flue pipe sizes.  There are clearance regulations for wood burning stoves, both the actual stove and flue components. There are also regulations and approval codes on indoor stoves, which I would guess are not on your outdoor fireplace.
I would encourage you to read the following: http://www.nfpa.org/catalog/TOC/211-13-toc.html