Measurements would be helpful on the shoulder diameter of the case and the inside or outside diameter of the neck itself, specifying which. An expample is: The neck is .338 is not helpful - the I.D. is .338" or the O.D. is .338" is helpful.(or whatever the numbers might turn out to be.)
1st impression to me, is that it is .30 cal, ie: the top part of a .308 (7.62x51mm case) or possibly a 7x57 Kort Net (Boer War short neck 7x57) case, or 7x57 or 8x57 with shortened neck. The shoulder angle appears to be around 20 degrees which is a common size for many different calibers. Suffice to say, if this ctg. case is original to the flask, the flask can not be more than 110-115 years old, probably.
I would also hazzard a guess at Middle East. It just seems to have that 'flavour' & if so, could easily have been made for use in a firelock or caplock, in the 1890's or early 20th Century.
The diameters requested above will allow positive identification of the ctg. if that is required. It does not look to be .45 cal. to me at all, as the rest of the flast must be HUGE in that case.