There aren't any validators on the platform - she will need to exit the barriers and re-enter. Most services to Finsbury Park use the higher-numbered platforms (9 to 11) that are behind a separate barrier line in any event.
It may be quicker to use the Victoria line to Highbury & Islington and change there for a service to Enfield - it's a cross-platform interchange at H&I. Admittedly it's a fair way from the National Rail platforms down to the Victoria line at Kings Cross, especially if you follow the signs rather than
taking the shortcut.
Alternatively she could take a Thameslink service from St Pancras across the road - these are more frequent than the services from Kings Cross which are (generally) only half-hourly.
If she has a Senior Railcard, she could get it added to an Oyster card at any Tube station for a 1/3 discount on the fare (if off-peak).