How do you infuse the flavor of a sauce into chicken? I have cooked some chicken in a pot with honey sauce. The sauce was very flavorful, and while the chicken had a great texture none of the sauce's flavor was in the chicken! It was almost flavorless.

I have seared the chicken and put it in a covered pot with some wine and honey as sauce (sauce covered about eighth of the chicken?). What can I do next time to infuse the flavors of a flavor base together with chicken when it is pot cooked?
You can't do it, it's physically not possible. Your meat will always taste of meat, not of sauce. Meat is not some kind of sponge which can soak up sauce, it's a dense muscle. 

If you want more flavorful meat, you can buy more flavorful meat. Most meat you can get in the supermarket is tasteless, because 1) people don't really like meat flavor if they are not accustomed to it (see the recent mutton question), 2) it's cheaper to raise tasteless meat (young chicken vs. soup hen) and 3) you need a fattier meat to have more flavor, but people prefer lean meats nowadays. Still, the meat will then taste of meat, not of sauce. 

If you find your food way too tasteless, you can also consider preparations such as a meatloaf, where you can physically mix spices into the protein.