Ah, I think the flexibility thing may be referring to the Airport Advance fare. Unfortunately, this is for TransPennine trains only.
As jt82 says, the train will either be via Piccadilly or Crewe, and it's unlikely your connection from the airport to either of these stations will be booked on a specific train.
In that case, the only thing you can really do is ask the guard before you join the London train. It's unlikely they'll say yes, to be honest, unless the trains are disrupted.