Yes, tor raises flags on Instagram's side, but most of the time you shouldn't have problems as long as you have cookies or access to the IG account's email.
The best way to stay anonymous (without joining the tinfoil hat society) is to use public wifi from an operating system like Tails or Whonix, then connect through tor to a logless VPN paid in bitcoins from a virgin wallet that have been directly deposited from a tumbler.