There are running themes in the show. I realize that Kate's plane and Claire's plane are very different models but I do still think that the same idea holds true...(Someone else had a plane in their flashback..one of the guys..I can't remember who it was if anyone can figure this out I would appreciate).

The plane is a child's toy, children are the essence of innocence. Many of the castaways are dealing with issues of having their childhood taken away from them, in essence their innocence was ripped out (Sawyer...Jack..I am guessing we will see Boone and Shannon dealing with that. Charlie, Walt lost his mother).

If "the man that she loved" is her father which so many of us believe and she killed him *either on purpose or accident it works either way* Kate lost that innocence. Perhaps she is on a journey to reclaim it...that is why she is holding the plane so dear.

The other person who I know had a plane in her flashback also is Claire and we know her entire story is about making sure that she can have a life for her child.

I know this isn't some huge theory and it's probably not even that a big one..but I think it might be the common ground they all share.