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Se convierte en un diálogo fluido. How would you translate this into English?

It becomes a fluid dialogue.
It takes on a fluid dialogue.

Are there anymore options?

It becomes a fluid dialogue works and is grammatical. But I might say:

... the dialogue becomes more fluid ...
... the dialogue flows better ...

The verb to take on is very similar in meaning to to become, but it is not always interchangeable. For example:

Something can take on a certain property or attribute.
Algo puede empezar a exhibir cierta propiedad o atributo.

Through the years, the old handsaw [took on a dull glow] that made it look alive.
Con el paso del tiempo, el serrucho viejo [asumió un leve resplandor] que le daba la apariencia de vida.
(my translation might not be all that good :))

How about?
 

It becomes a smooth dialogue.

Even better than what I said.

¡Gracias, David y Marsopa!