Flynn, retired hurt Friday on four after missing a hook off a James Anderson bouncer which led to two of his teeth being removed.
He didn't bat again Saturday as New Zealand, nine wickets down, were bowled out for 381.
Flynn then didn't take the field, with twelfth man Jeetan Patel on in his place, as England slumped to 152 four, a deficit of 229, at stumps.
"He's back at the hotel and won't field," team spokesman John Durning told reporters after Saturday's play.
"Before he comes back he'll have to some gym work just to see how pressure affects him.
"If he's not right he won't bat. There's not any reason to suggest he won't be able to bat. But we thought we had him right before lunch but then he got a bit queasy."
Durning added: "He's had a scan and that was all-clear and that's the main thing, so he's got no damage."
Left-hander Flynn, 23, playing in only his second Test, had felt nauseous and vomited overnight. He fell ill again Saturday and, although concussion had initially been ruled out, team officials decided he should see a specialist.
Northern Districts batsman Flynn had to endure two hours of dental work Friday after being hit by Anderson and retiring hurt on four.
Although he was wearing a helmet, the ball appeared to force the grille into his face with his side then 136 for four.
A top front tooth was knocked out by the initial impact and a badly cracked bottom tooth was also removed Friday.