There is usually a very slight pause between fin and à un conflit but all these vowels might be also pronounced in a row.
In poetry, hiatus tend to be avoided but in regular prose/speech, French has no problem with successive vowels, whether nasalized or not.
For example, the sentence:
Tu as en haut un houx aérien.
has eight successive phonetic vowels /ty a ɑ̃ o œ̃ u aerjɛ̃/ but can be nevertheless easily pronounced by any native French person.
Here is another one that could technically be heard in a primary school:
Haie a un A, un I et un E et eau a un E un A et un U qui se suivent.
/ɛ a œ̃ a œ̃ i e œ̃ ə e o a œ̃ ə œ̃ a œ̃ y kisəsɥiv/
Nineteen phonetic vowels...