In general, you risk your account being banned if you use Flume to infringe upon Instagram's Community Guidelines. Using Flume does not pose an account security threat, as great care is taken to protect your privacy and develop high-quality software that is indistinguishable from the official applications. The same cannot be guaranteed with other third-party apps and websites, and your usage of them puts your account at a much greater risk than using Flume.
Flume has been available publicly since September 2015, and in private development since December 2013. At time of writing, 0 accounts have been banned through their use of Flume. This also includes around 20 test accounts that are used heavily during development and testing and exhibit non-standard, repetitive behaviour.