How can I find flavors that pair well with a given ingredient?
First, a caveat: different people and different cultures have different tastes, so no pairing recommendations are likely to be perfect for you. 

Books

You can find books on this topic, for example by searching for flavor pairing on Amazon. A couple of the most popular ones:


The Flavor Bible - for each ingredient, lists a large number of other ingredients that pair well with it, with the best/most popular ones highlighted. Also includes a small number of example ideas of dishes and several-ingredient combinations.
The Flavor Thesaurus - for each ingredient, lists a fair number of good pairings, each with a bit of additional description and perhaps recipe ideas.


Websites

There are a few websites discussing this sort of thing:


IBM's Chef Watson - lets you pick an ingredient, then suggests others, which you can accept or reject to get additional suggestions. Also provides example recipes. Free.
Foodpairing - lets you pick an ingredient, then suggests "matches". Free version has a limited set of ingredients, and for a monthly fee you get everything.
VCF 2000 - a commercial database of volatile compounds in foods. It has a demo, but the actual database is extremely expensive (currently $2775). Between that and the difficulty of basing things on aromatics, it's probably not particularly useful, though.


On pairing by aromatic compounds: while folks have used this to come up with ideas, it really seems to be at best an oversimplification. Plenty of things with "matching" aromatics don't end up being good pairings, and plenty of commonly liked pairings have very different aromatics.

Do it yourself!

Searching for recipes is actually a pretty effective method here. Just search for "X recipes" on Google, or search for X on your favorite recipe site, and look through the recipes to see what other ingredients people use with X. You'll quickly come up with lists of ideas quite similar to those you might find in dedicated books or websites.