I have a Pit Boss Lexington grill. The lowest temperature setting is smoke which is about 50-160 degrees. The setting above that are marked in degrees. I was using trager apple pellets. I had a skinless, boneless chicken breast. I cut the breast in half and used a dry rub on one piece and nothing on the other. I smoked it for about 3 1/2 hours on the smoke setting. I used the lower rack with a pan of water for moisture. Internal temperature was about 152 degrees. Not only was the chicken dry but it had no apple flavor. What did I do wrong?
As moscafj's answer correctly states, the lowest average temp on that grill is more like 180-200F so you annihilated that poor bird! Even though the final temp may have been 150, it was almost certainly much hotter than that at some point (if the internal meat was firm and white this is certainly the case). But also, the idea of "low and slow" for BBQing is because your typical BBQ meats, like pork shoulder and beef brisket have tons of connective tissue which breaks down over time, along with tons of fat which keeps things moist throughout the cook (because it slowly gelatinizes into deliciousness). Skinless breast has none of that and is notoriously hard to keep moist regardless of how you cook it.
So really unless you know what you are doing it's a horrible cut of meat to smoke -- and it certainly should never be smoked for that long regardless. Whole chickens should be checked after an hour with an average smoke temp of 200 and will probably be done by 1.5-2 hours. In practice, since opening smokers is undesirable (you lose a lot of heat), you should have an oven-safe type thermometer so you always know what temperature the meat is. Ideally, have one with multiple inputs so you can monitor multiple zones in the meat and/or also monitor the temp of the air in the grill.
Additionally, apple wood is not a super strong flavor to begin with, but it's also important to keep in mind that smoke adheres and penetrates the meat best when it's cold and stops "sticking" to the meat once the outer layer gets fairly warm (and pretty much stops doing anything good after 130-140). Given the grill temp you would have hit that fairly quickly and thus the smoke really was only flavoring the meat for ~30 mins. This is why when you are smoking something like pulled pork you are only trying to get the good 'blue' smoke for the initial hours of the cook and after that it's much more about applying low and slow heat to bring the internal meat to temp -- you really don't want to be smoking it the whole time. In fact, it's often bad to do so because smoking can quickly go from adding a nice flavor to adding a lot of bitterness and unwanted flavors if you overdo it.
So TLDR, wrong cut, wrong amount of time, and wrong temp.
I'm not sure where your numbers are coming from. According to the Pit Boss Lexington manual, the lowest smoking temperature is 200F (about 95C). It looks like your temperatures are off. Also, three and a half hours to smoke a chicken breast sounds like a really long time. Essentially, it appears that you've overcooked your chicken.