Something doesn't add up on the FDR trace.
I've fine-pencilled / ruler'ed it. The first event appears to be the uptrim on #1, at 2:52:34. Increase in FF, ITT and Obj Tq. Once the Obj Tq on #1 reaches 100%, at 2:52:37 there seems to be a simultaneous Master Warning #2 Flameout, start of rise in Beta 2 (feathering), and a simultaneous drop in all #2 parameters, except the FF, ITT, NL and NH, which drop then stabilise (presumably at idle?) - so no ACTUAL 'flameout'.
The #2 looks like it didn't autofeather until 3 seconds AFTER the uptrim on #1 - and there doesn't seem to be anything in the trace that precipitates the #2 autofeather?
Shortly after that, #1 throttle is retarded about 10 deg. Not unusual I would suggest if they were having directional control problems. However, it is then progressively retarded (and at one point, the #2 throttle firewalled?) until the Fuel Shut Off is activated at approx. 53:15:22. Unlike the #2, the flame DOES go out in #1.
#2 turbine is running throughout.
In the last few seconds, it looks like #2 starts to unfeather (increase in Beta) - this seems to coincide with the #2 throttle being pulled back. #1 stays feathered throughout, although appears to relight as soon as the Fuel Shut Off is cancelled.
Seems like an odd sequence of events to me?
I think that ENG #2 lost power and rolled back to a state of around idle or so, this triggers the ATPCS sequence which is activated by ENG #2 producing less than 18% TQ, ATPCS immediately uptrims ENG #1 to RTO, closes bleed #1, and after a delay of 2.15 seconds feathers ENG #2. This is all just as it is supposed to be.
As I read the DFDR data engine #2 suffered some sort of malfunction, but not necessarily a complete flame out. In any case the warning will be ENG FLAME OUT.
It seems that the crew proceeded to retard PL1, and move CL1 to FEATHER and then FSO.
The increase of Beta #2 at the end could be produced by moving the Power Management selector away from take off, which cancels the auto feather signal, and as CL #2 was never moved to FSO Prop # 2 will start to un-feather. A highly undesired status.
Moving the Power Management selector away from take off is a normal thing to do if attempting an airborne relight. But only if all preceding procedures have been completed correctly.
Unfortunately it seem the crew were thoroughly confused, and shut down the operating engine.