Yes, you can progress to a new tier either by collecting enough Tier Miles, or by taking enough qualifying flights.
The thresholds for each tier are as follows:
Silver: 25,000 Tier Miles or 25 qualifying flights
Gold: 50,000 Tier Miles or 50 qualifying flights
Platinum: 150,000 Tier Miles only
This means that even if you don’t manage to collect enough Tier Miles because you generally fly short distances, you can still move up a tier because you fly frequently.