Square Enix has published a separate video explaining the order in which Kingdom Hearts games should be played

Although the Kingdom Hearts series has only three parts, its stories can be very complicated due to numerous spin-offs and a confusing storyline, so Square Enix has published a separate video explaining the order in which the games should be played:

Here's What We Know

So, first, you should play through Kingdom Hearts HD 1.5 + 2.5 Remix: this collection includes the first game, Re:Chain of Memories, Kingdom Hearts 2, and footage from Kingdom Hearts 358/2 Days. Next, it is worth taking up Birth by Sleep Final Mix - the prequel contains an important backstory of the series. After that, you should play Kingdom Hearts HD 2.8 Final Chapter Prologue, which includes Dream Drop Distance, Kingdom Hearts χ Back Cover, and Kingdom Hearts 0.2 Birth by Sleep - A Fragmentary Passage. And finally, after that, you can start playing Kingdom Hearts 3.

For those interested in the chronological order, the video also covers that aspect.

Source: GamingBolt