First of all, really sorry for the delayed response. Support crew is on summer vacation thus it causes some delay on replying inquiries.
I left alone and trying to catch up. But, starting from August 15, vocations will be over and this problem will be resolved. Everything will be get back to normal like before. Normally our support-get-back time is within 2 business days.
No, that icon is not a part of Flexible Template. It is a part of Core Joomla itself. Why do you want to disable that icon?
You are seeing it only because you have the "Administrator" access, nobody beside you will see that icon in there. Is it really annoying you? If you insist on hiding that icon; check this topic:
forum.joomla.org/viewtopic.php?t=267704
Regards.
Support