My perspective is that we can't know precisely what Charles was thinking or what he meant when he made those comments that obviously irk Spencer.
I'm not defending Charles, simply trying to be objective about an emotive subject. I think it's well understood that people in shock sometimes do - and say - things that seem at odds with the gravity of the situation. On the other hand, it's also known by most that Charles took a rather pragmatic 'approach' to his early relationship with Diana - in spite of the media attempting to portray it as some kind of fairy tale romance.
When he said, "she'll be forgotten soon enough" I'm guessing most people - and certainly Spencer - believed he meant that he would soon forget her. Maybe he did - however, it's also possible that he made the observation in a 'world-weary' cynical way. I don't know and I don't think anyone can say for sure why he said that or what he meant by it; although those that really dislike him will insist otherwise.
What puzzles me more - because I'm interested in human behaviour - is why Spencer decided to write this 'tell-all' book. I understand he feels protective of Diana and maybe the drive to 'put the record straight' is now his mission in later life, but I'm surprised it doesn't seem to have occurred to him that, in doing this, he'll also put his sister back into the spotlight. She may well have been "The people's Princess", but not for everyone. To some, her erratic behaviour and her subsequent affairs provoke less than flattering observations.
If he's attempting to highlight the dysfunctionality of the RF 'life', and to stick it to the King - is he not aware that the similar dysfunctionality within his own family, not to mention his serial-marriages, will also come under the spotlight? If you think about it, historically nobility, the aristocracy, royalty, have always to some degree or other been somewhat flawed and maladjusted.
I just don't know what he hopes to gain from this book. Maybe it would really have been better to allow Diana to simply RIP.