Does the "CDC Planes Grounded" emergency event prevent the First Responder's ability?
CDC Planes grounded states

Players cannot move by direct, charter, or shuttle flight (or the event airlift).

The First Responders ability is

• As an action, you may move to any city with a research station.
• Immediately after an Epidemic, you may – out of turn – move to the epidemic city and Treat Disease there (before Infections).

Neither of these abilities are a direct, charter or shuttle flight, and so should not be affected by planes being grounded.
This thread on boardgamegeek comes to the same conclusion.