Assuming the Flames do not acquire any additional draft picks before the 2018 NHL Draft, they will not have any picks until the fourth round. This has never happened before.
In fact, the Flames have only had one season in which they had no draft picks in the first or second rounds: 2010, when they selected their first pick in the third round. Otherwise, every single year, they have had at least a first or a second rounder.
Their most recent draft without a first round pick came in 2015, when the Flames ended up with two second round picks to open up with.