The following is all my opinion/speculation:
I agree with many that he just didn't want to go to school, and he "found" a place, close to home, where he thought he could hangout and stay warm. maybe he had plans to spend a lot of time there over the next few months, or until he got caught. maybe he was going to rob the place. I doubt it, though. if that was his goal, breaking a window would have been a lot easier. He was trying to stay unnoticed.
I also think he probably waited until it at least started to get light out before climbing the antenna. Also, there was a lot of snow on the ground, but the roof almost had to be clear of snow. I don't know how long the Dilly's have lived there, but I'm sure he has fantasized about climbing that antenna for some time. It wouldn't shock me if that hadn't been the first time he's been on that roof. He obviously went up there with the intention of climbing down the chimney. Had he looked down the chimney before?
Without knowing more specifics and details, my theories could be way off, or even impossible. But I'm basing them on the assumption that that chimney was the same size all the way down to where it "ended" at the floor level of the second story. Also, what, and where, was the flue? It sounds like it was just a hole in the side of the chimney. Where would it be? Somewhere towards the ceiling of the second story. Let's say it was six feet above the floor. I'm sure it had some kind of a cover on it, but he was apparently able to open, or remove, the cover.
So he climbs up on the chimney (wearing both his coat and glasses) and sits on the edge with his legs dangling inside the chimney, and slowly starts to lower himself into the chimney. Now I can't decide if I think that he was able to descend the chimney in a controlled manor (using his feet, knees, butt, chest, back, elbows, and hands to leverage against opposing walls), or if he passed the point of no return, couldn't pull himself back up, and eventually had to let go and fall the twelve or fifteen feet down to the second story floor, but either way he ended up at the bottom. I also feel that his coat was likely pulled off as he descended. Especially if his arms were extended above his head.
So now he is at the bottom of the chimney, and realizes he is in big trouble. He may even have a broken ankle, or something. Even if he was able to safely descend into the chimney, I envision the space being too small for him to be able to get enough leverage to climb back out. I think it COULD be possible to climb out if he had more room, but sadly, that space was just so small. You really need to almost be able to bring your knees up out in front of you.
My best guess is that his arms were over his head. Or, if his arms weren't initially over his head, he was able to get them up there. So he felt the flue opening (that I'm assuming is about six feet above the floor) and opened the cover. I believe he pushed his coat and glasses through the flue (that was above his head) in hopes that someone would search the house and see them. God, I hope he didn't do it while thinking he was doing it so they could find his body. It was actually a really smart thing to do. Sadly, it wont bring him back, but I bet that he would still be missing if he hadn't done that. Even if they searched that house, they still probably wouldn't have found him. Who knows? He may have NEVER been found otherwise.
On another note, I have to disagree with the criticism of law enforcement in this case. They did their best. There were NO signs of foul play, and he could have been ANYWHERE within 1000 miles of home. It was just a freak accident, with freak circumstances. I know the critic's hearts are in the right place, and it is frustrating and shocking how close to home he was found, but think about the thousands of other places that the police DID look for him.
That does bring me to another thing, though. I'm not sure that I'm buying the official cause of death. Again, this is assuming that the entire chimney was a constant 9 x 13 vertically all the way down, but unless he initially entered the chimney with his knees tucked under his chin, I don't think it would be possible for him to get his legs folded up against his chest once he was inside the chimney. Also, I'm not even sure it would have been possible for him to enter the chimney with his legs folded up, and it seems like a very unusual way to climb down into something anyway. So assuming he is basically standing in the chimney, I don't see where the compression on his chest would come from. So how did he die? Well, one thought is would he eventually asphyxiate from a lack of oxygen? Did the chimney eventually fill up with his expelled breath, and there wasn't enough airflow to circulate the air and replenish the oxygen? I'm not even sure if this is a feasible explanation (especially when assuming that the flue hole would only help circulate the air). So what are the other options? Dehydration or hypothermia (not sure how cold it was in there) are really the only other two that I can think of.
So why would the authorities lie about his cause of death? Well, I can think of several reasons. First, what ever way he went was undoubtedly unpleasant, it just seems easier to accept (for everyone) to believe that he went relatively quickly as opposed to living that horror for four or five days, or so. Second, it also avoids the criticism and negative public sentiment where people could have said that the police COULD have saved him if they were better at their jobs. Third, I think it should prevent any kind of lawsuit from the family. It just makes things so much easier on the police if they can claim that he was already dead before he was even reported missing.
That being said, most likely the official cause of death is true. I'm generally an advocate of truth, but I wouldn't blame them if they were trying to cover this up to prevent bankrupting the town with a frivolous lawsuit. I personally don't feel that law enforcement screwed up. Again, it was just a freak accident with freak circumstances. Very sad.