The initial meaning of this arrangement of words is found in connection with the weather; the subject of the verb is invariably “wind” (vent) or some such entity that connotes the wind; in saying “le vent chasse les nuages” you are saying that the wind pushes the clouds away and thus finally clears up the sky.

There does not seem to exist a real idiom but an image, a figure of speech people ressort to in various ways. The word « nuage » used by itself keeps the meaning it has in the expression, that is the figurative meaning of “element that casts a shadow over something, that impairs somewhat its normal evolution”. Here is a case of that (
linguee1);

• Biarritz n’a pu dégager le ciel de tous les nuages qui menacent le projet d’approfondissement de la démocratie dans l’Union européenne. (europarl.europa.eu)
  Biarritz did not manage to dispel all the storm clouds attending our mission to promote the democratisation of the European Union.

One should say, pertaining to the style of the above sentence, that it is awfully flawed, as “le ciel” has no figurative raison d’être in that sentence; it is nevertheless a telling sentence.

Here is a case of figurative use of the whole expression (linguee2);

• Dès lors, afin de chasser les nuages qui pourraient assombrir la Commission en la matière, je pense que des arguments plaident […]
  So in order to clear up the cloud that could hang over the Commission in this matter, I think there is a case for further […]

Here is another instance in which “chasser” is taken literally as meaning “hunting for something” (as trainspotters do), the idea being that the contemplation of clouds is a spiritual activity (ref);

We find in that source a reference to the use of the word « nuage » as referred to above;

• « Avoir un nuage au-dessus de la tête », « pelleter des nuages », « entrevoir un avenir chargé de nuages », « voir passer un nuage dans les yeux de quelqu’un » : autant d’expressions péjoratives associées à ces formes mouvantes qui surplombent nos univers, alors qu’un ciel bleu – ou sans nuages – est symbole de bonheur paisible.

• Ce n’est qu’une question de perspective, croit l’auteur britannique Gavin Pretor-Pinney, cofondateur de la Société d’appréciation des nuages (Cloud Association Society – CAS) qui regroupe des milliers de membres dans le monde. Tous ont en commun cette volonté de lever les yeux au ciel pour en admirer les beautés. « Adulte, les nuages deviennent un paysage si familier que nous ne les voyons plus. Les seuls moments où ils captent notre attention sont lorsqu’ils font entrave au soleil », fait-il remarquer.

Of course, this particular meaning has to be dissociated from that of the expression with the figurative sense; while we retain the lesson it gives us as concerns the meaning of the figurative “nuage”.

Getting back to the general figurative meaning, according to yet another source (ref) the expression can be taken as meaning roughly “to clear up the impression of being physically unconfortable”.

I wouldn’t therefore speak of an idiom but rather of a general figure of speech, the meaning of which can be stretched to fit different contexts in which the figurative meaning is always something pejorative.

Non, ce n’est pas une expression idiomatique mais il peut s’agir d’un procédé littéraire.

Il a la tête dans les nuages.

Toutefois, les précisions apportées dans les commentaires suggèrent que le personnage est pensif.

@petitrien The book is Aurélien by Aragon again (published in 1944). Before the quote I gave there was a long boring monologue by the first character about something business related; the last sentence is him breaking off from that topic to say “Voyons, c’est sérieux…. Il eu l’air de chasser des nuages.” Afterwards the second person says “Tu dis ?… Excuse-mois… Je t’ai assez mal suivi…”. Sorry for not giving it beforehand in my question, it just didn’t seem relevant to me, and as a rule I prefer an answer which depends least as possible on the context. Thank you.

La phrase « Il eu l’air de chasser des nuages » pourrait révéler le point de vue du personnage ayant parlé « il (l’autre personnage) a la tête dans les nuages » plutôt que de caractériser son état d’âme « il écarte tempo­rairement ses préoccupations », mais sans certitudes.

In English:
No, this is not an idiom but it could be a literary device.
Nevertheless the details you have added suggest that the character is lost in his thoughts.
The sentence il eut l’air de chasser les nuages might reveal the point of view of the character who had been speaking (A) “he (B) has his head in the clouds” rather than characterize his state of mind “he momentarily blows away his worries”.

En outre, on peut représenter des idées de différentes façons. (Besides we can represent ideas in different ways.)

Il pleut des cordes.
It’s raining cats and dogs.