Is there a suggested viewing order for the Trois Couleurs trilogy?

Individually the stories are not dependent of each other. You can watch any of those movies in any order, and you will not be clueless about the stories.

But, I think it's better to go in the order they were released ie, Blue, White and then Red. Red, in a sense gives an ending to all the three movies at the end. So, in my opinion, it is best to watch Red at the end.

No "obligatory" order, according to the director himself. He seems to have intended to make them in the viewing order, but concedes it all falls down to the viewers.

In an interview for Positif (a French cinema magazine) in 1994, Kieslowski declared:

J'ai réalisé ces trois films dans l'ordre, pour permettre au spectateur de les voir lui aussi dans l'ordre, c'était comme un signe, mais ce n'est pas nécessaire. Ce sont trois histoires séparées, bien que liées et évoluant ensemble. Je respecte beaucoup mes spectateurs et je leur laisse la liberté de les découvrir dans l'ordre, de n'en voir qu'un seul ou même aucun !

Bien sûr, il y a une progression, et pour accéder à d'autres significations, il faut tirer le deuxième, le troisième ou le quatrième rideau. Mais il y a aussi le premier rideau, et là, c'est juste une histoire. Je n'ai jamais pensé à un triptyque comme en peinture ; plutôt à trois nouvelles rassemblées dans un même volume. On pourrait imaginer qu'un auteur les aurait écrites pour un hebdomadaire et ensuite publiées dans un recueil.

Bien sûr, les spectateurs peuvent être amenés à établir des correspondances ou des liaisons entre ces trois films. D'ailleurs, si l'on étudie les entrées en salles, on se rend compte que lorsqu'un nouveau film de la trilogie sort, pendant deux semaines les spectateurs du précédent film augmentent. Si le même phénomène se produit pour Rouge, cela voudra dire que le public aura envie de découvrir des choses nouvelles.

Here's a translation, courtesy of DeepL, which I found pretty accurate:

I made these three films in order, to allow the viewer to see them in order too, it was like a sign, but it's not necessary. These are three separate stories, even if they're linked and evolving together. I have a lot of respect for my spectators and I give them the freedom to discover them in order, to see only one or even none!

Of course, there is a progression, and to access other meanings, you have to draw the second, third or fourth curtain. But there's also the first curtain, and this is just a story. I never thought of a triptych as in painting; rather three short stories gathered in the same volume. One could imagine that an author would have written them for a weekly newspaper and then published them in a collection.

Of course, spectators may have to establish connections or links between these three films. Moreover, if we study the admissions, we realize that when a new film in the trilogy is released, for two weeks the audience of the previous film increases. If the same thing happens for Red, it will mean that the public will want to discover new things.

Unfortunately I can't provide a scan of the original interview, but it got quoted in this mémoire from Cécile Desilles. A mémoire is a thorough piece of writing French students have to turn in to validate their Master's degree, and this one was reviewed by the ENSCI, a rather well known design school. Hence, I think the transcript is legitimate.