Answer: will arrive
Step-by-step explanation:
Would is the past tense of will yet both verbs can sometimes be used interchangeably.
Generally, will and would differ in use depending on the certainty of the event. If the event is a hypothetical that would have resulted in another outcome, would is used and if it is certain and is still to occur, will can be used.
In this instance the speaker believes that taking the flight will result in them being late which makes it a future certain event so will is used.