Napier: Flynn received a blow to his left hand while scoring a defiant 67 in the 10-wicket first Test defeat and he was unable to bat in the nets Tuesday or do fielding drills at training ahead of the Test in Napier starting on Thursday.
His injured hand was scanned Tuesday and no broken bones were revealed, but deep bruising and ligament damage made holding a bat difficult.
The 23-year-old will continue to receive treatment and will be assessed Wednesday before any decision is made on whether he plays in the Test.
Team management said How would join the team late Tuesday, after being dropped from the national team during the one-day series against the West Indies in January.
Jamie has since scored 190 for New Zealand A against England A and hit some big totals in domestic first-class cricket.