We have seen the trailer in their black space suits but Miles Teller has confirmed that the original costumes from the comic will be making an appearance. Basically he says they will evolve throughout the movie and the black space suits won't be the only costumes we will see. How much time we see them in the iconic suits is unconfirmed. ScreenCrush talked to Miles Teller and he gives us some detail into what we will be seeing in the movie:
These are the beta versions of the costumes, which is great [...] But, yeah it would be very odd if the Fantastic Four didn't don the traditional costumes. You've got to. There is some servicing there. You've got to give that to the fans. That's what it's all about.
Watch the trailer below: