Complicated question, but a good one. First, realize that the primary two ingridients of all candy are sucrose, C12H22O11, and fructose, C6H12O6. You can type either sucrose or fructose (or any of the other chemicals) into google image search and many of the results will be their chemical structure.
Regarding the flavors, many of the specific formulations (e.g. skittles) are obviously trade secrets. Many flavors are known, however. For a general article about how organic chemists come up with flavor chemicals you can read http://www.chemistry.org/portal/a/c/s/1/feature_tea.html?id=c373e9f86cf08f208f6a4fd8fe800100
For a slightly more specific articles about how many candies are flavored you can read: http://www.ccmr.cornell.edu/education/ask/index.html?quid=148
For an example of some very common chemicals, check out the Smell and Taste sections of http://en.wikipedia.org/wiki/Flavor
Lastly, for a huge comprehensive list that DOESN'T tell what the chemicals smell/taste like but basically includes almost all the chemicals used in flavoring, check out: http://www.flavornet.org/f_odorants.html
Again, any chemical you can type into the google image search and it will show you its structure. Most mint flavors (e.g. wintergreen) are synthetic chemicals such as methyl salicylate, ethyl salicylate, etc. However peppermint in particular is usually an oil extracted from plants.
And lastly, if you enjoy this kind of stuff, realize that you can become a chemist, and that these jobs pay fairly well, especially if you have a good nose/tongue. You can go into the flavoring industry, perfume industry, etc. Good luck!