The Flues top tang screw is an odd one.
It's a short stubby wood screw and simply screws into the wood under the top tang. The wood is not very thick there due to the action design.
There is no action screw up front that goes completely thru from top to bottom trigger plate to hold things together.
The rear tang screw does, but that doesn't lend much support to the action and head of the stock .
The rear tang screw is pretty small in dia as well and can often be found w/stripped threads.
So the Flues top tang screw causes problems, mainly it gets loose and the action rocks upward on recoil. The action is usually a loose fit against the wood.
The top section of the stock 'ears' are often cracked or broken and reglued as a result on many Flues shotguns.
A crack at the top of the grip right behind the tang is also frequent.
You can't simply put a long top tang screw down thru the stock and action to screw into the trigger plate as there are locking bolt mechanics in the way.
I have overcome the problem by using a machine screw in place of the wood screw.
On the inside of the stock inlet, the underside of the wood where the wood screw enters is easy to get at. The wood is not all that thick there but making a small steel plate of 1/16" steel and D&T it for the machine screw works to hold the assembly together much better than the wood screw.
I epoxy the plate into place in a shallow inlet in the wood to hold it in place for assembly.
The machine screw (a #8 works IIRC),,maybe a 10) & using a fine thread, there is plenty of holding power. The screw head is shaped to fit the countersink in the top tang and all looks fine and dandy
I install the screw and plate with a tiny bit of 'draw' to it to pull the action back into the wood upon assembly. That is the only thing that actually keeps the two componenets tight.
It doesn't take much,,a 1/64" is plenty. Move the screw hole in the direction you want to pull the metal along with it.
It's a weakness in the Flues. Glass bedding along with this has kept them is shooting shape for me but I always told people to use soft recoiling loads or the design was likely to
show those weaknesses again under heavy recoil and use.