However, as many of you who have seen the special have discovered, the existence of these cameos skews the timeline for MK and DC as we know it. In this topic I'll detail the problems and the problems with suggested solution reasoning.
First a bit of background on the original Magic Kaito chapter, "Kaitou Kid's Busy Holiday". The chapter itself was written some time during or before 1988, quite a few years before Conan first started appearing in Shonen Sunday. While both MK and DC's timelines are difficult to accurately pinpoint, we do know that certain events in both stories must take place at specific times.
What we do know must be true about the timelines:
1) Kaito learns about his father and becomes the Kaitou Kid sometime before Shin'ichi shrinks.
Proof: Kaito as Kid does the clocktower heist and unknowingly battles wits with Shin'ichi, after Shin'ichi has begun to gain a reputation as a high school detective.
2) The Black Star heist is Conan's first interaction with Kid.
Proof: Seeming to have forgotten that he almost stopped Kid as Shin'ichi, Conan asks Agasa for more information during the Black Star heist. Of course, his forgetfulness could be because he had never heard of Kid being referred to as Kaitou 1412 before. He had only battled wits with Kid once, so it's possible the name just slipped his mind. During the clocktower heist Shin'ichi also didn't know Kid practiced stage magic (he simply saw through one trick) so it's not strange for Conan to not know much about Kid during their first encounter, despite meeting before.
3) The Black Star heist occurs sometime after the clocktower heist.
Proof: The clocktower heist is presented as a flashback. Kaito remembers the heist as he prepares to fly over to the Haido City Hotel on April 1st.
4) Haibara doesn't appear until a long time after the Black Star heist.
Proof: The Black Star heist occurs in volume 16 of DC; Haibara's introduction and first interaction with Conan doesn't appear until volume 18.
5) The Angel Crown heist occurs before Kaito has learned about Pandora.
Proof: The Angel Crown heist occurs in MK volume 1 while Kaito doesn't learn about Pandora until the Blue Birthday heist in MK volume 3.
Assumed about the timeline:
The Black Star heist occurs after Kaito has learned about Pandora.
Reasoning: It's highly likely Kaito by the time of Black Star has learned about Pandora and begun searching for big gems, but we can't be certain since we don't know at what point during the MK timeline Shin'ichi is shrunk to become Conan. All we do know is that Kaito becomes Kid sometime before this occurs.
Now for the problems that make our heads spin...those cameos in "Kaitou Kid's Busy Date".

Problem 1:
During the animated version of the Angel Crown heist, Kid disguises himself as Conan at one point and even says "There is only one truth". If this sight gag is taken seriously, it means Kid has already performed the Black Star heist and thus met Conan.
Solution: Impossible. During the Black Star heist, Nakamori knew about Kid's use of the hang-glider cape and seems to be accustomed to Kid's movements and tricks (but still unable to catch him) and is used to checking people's faces to see if they're Kid in disguise by tugging on them. While the animated version of the Angel Crown introduces the hang-glider cape prematurely, Nakamori is clearly surprised at the use of it and didn't really know about Kid's disguising abilities yet.


Problem 2:
The Detective Boys and Conan are shown at Tropical Land during Kaito and Aoko's date, suggesting that the Angel Crown heist takes place after Shin'ichi has shrunken and become Conan.
Solution: Majorly and utterly impossible for one simple reason: Haibara. As I pointed out earlier, the Black Star heist occurs long before Haibara's first interaction with Conan. If we assume the Black Star heist occurs after Kaito learns about Pandora, the Angel Crown heist must take place quite sometime before that, for reasons pointed out during Problem 1 above.
In short...
Don't wrack your brain coming up with excuses for the animation staff. Ignore the cameos and just consider them Easter Eggs; they are not meant to be taken seriously.