Flynn had been on the non-football injury list and did not practice at all in training camp. Given the time he spent in Foxborough -- he was signed in early June -- he presumably has some understanding of the offense, and would probably be a better emergency option than Lindley.
For now, the Patriots must balance their quarterback reps in the preseason. If Jimmy Garoppolo is indeed going to start four regular season games, the Pats surely don't want to risk injury over the next month. It seems Lindley will be there purely for reps, and if he does well enough, perhaps they'll keep him on through the first four weeks.
Lindley ended up starting a playoff game last year for Arizona, which was decimated by injury. He went16-for-28 for 82 yards in a divisional round loss to Panthers.