The only flametop TBird 5-string I know of is this one I have.....but it ain't a Gibson and the flame is in the wood grain.
I haven't heard of a non-Studio Gibby 5 Tbird. Maybe an aftermarket respray to spiff it up (is it flames over a typical black one?) Is it definitely Gibson and not a converted/resprayed/retagged Epi TBird 5?
Maybe it was resprayed for Henry J. to use on a TV/trade demo and billed as "Gibson's Hot New Bass"
Suspicious that there is no CS decal or SN stamp if it really is from Gib CS and not aftermarket. Maybe a last minute respray/overspray for a NAMM or Frankfurt trade show in an effort to sell what proved to be a dead horse model...but you'd think someone would have a pic of that from a show/magazine if that was the case?
Several years back, there was a UK clothing chain that did a run of custom finish Gibsons and there were a couple of TBirds in it. I recall a 4-string with a Union Jack finish. I think there was a Studio 5 but do not recall what the graphic was. Some of them were cool, some sort of ugly. But I think the graphics were actually done with cloth material and then cleared over....and I am pretty sure they were done outside of the Gibson factory aftermarket.
I think used Gib Studio 5-strings go for around $1,000 used when they pop up.