I'd like to hang a rain chain, but not quite vertical straight down -- at a slight angle from vertical. What angle from vertical can I hang the rain chains, and still have them work? Are there any guidelines?
It's going to vary with design and rainfall rate. More flow means more likelihood of spillage and drop detachment, so it depends on your personal preference. Add to that the wind around your home and it's hard to say.
Trial and error are the best approach.
We just removed all the rain chains (of varying sizes) off a Federal building and installed regular downspouts. They all hung plumb and they were all about 36” from the building (large overhang). They all were less than 10’ long and they all failed because: 1) transfer of water from gutter to chains, 2) appropriate size chain to transfer water and 3) wind blowing water off chains.
While the system did not have sloped chains, any slope would reduce the area on each chain to carry the water. In addition, sloped chains would allow the water to run to the low side of the chain using only a portion of each chain to carry the rain. (The greater the slope the less of each chain will be used.) This partial wetting of the chains will cause mold and mildew on the chains. If it’s not dangerous, it will be unsightly. (Remember the Princess Diana memorial in London.)
Of major concern where I live, is the wind factor. The chains caused big problems by allowing the the water to spray the building, the entrance, etc. I’d reconsider the chain idea.