The AOPA Air Safety Foundation has gotten clear definitions of what flight training activities are currently permitted. While this is expected to change today, at the moment, VFR flight training activities are prohibited. That means primary flight instruction with student pilots is prohibited, and VFR flight training in pursuit of a certificate or rating is prohibited.
However, the FAA has confirmed to ASF that proficiency and currency flights by certificated pilots are permitted, outside of enhanced Class B airspace and TFRs. That means, for example, touch-and-goes, pattern work, and maneuvers in the practice area are permitted for certificated pilots (pilots with a recreational, private, commercial, or ATP certificate). Instrument proficiency checks and flight reviews are permitted. Any operations conducted for proficiency or currency as required by the FARs are permitted. Instrument flight training on an instrument flight plan and clearance is permitted.
Pilots are reminded, though, that VFR flight is still prohibited within enhanced Class B airspace and in temporary flight restriction (TFR) areas.