I'd been wondering for a while why the OP had used the word 'Catch' in the title of this puzzle rather than the more common 'Capture', as is the phrase usually - but now I understand, as the island in question is:
PIANOSA, the Italian island which provides the setting for Joseph Heller's satirical wartime novel Catch-22! The blue flag is to be found on the square numbered 22 (i.e. the third square in the third row down, marked by a completely blank playing piece) - i.e. we catch it in 22.
How to find this? First recognise what we're looking at here...
This is the game board from Stratego. This war-based game involves a set of pieces each representing soldiers of different ranks (and a bomb and a flag, but we shall ignore those for now). Their relative values in the game's scoring system will become important shortly...
Look closely at the pieces in the diagram...
In the top-left corner of each there is a symbol. If we extract the letters relating to specific symbols row by row, we get the following sets of characters (I shall represent empty spaces as underscores):
Red circle: EMCPEK
Red 3 lines: RNKO
Red triangle: ORR
Red cross: EERDELD
Red diamond: R_EDYOC-LEVE_
Red shield: UOSOMD
Blue star: JMRJRARAOO_O_AMJM
Blue moon: TYALNE
Blue teardrop: RFYAA
Blue square: RWNE
Look at the letters associated with the blue star symbols first...
These are an anagram of MAJOR_MAJOR_MAJOR. Now the penny drops! Heller's characters in the novel often have very strange or comical names - this is clearly a reference to Catch-22 and the character of Major Major Major Major! In fact, all of the letters sets above form anagrams of different characters in the book!
Red circle: EMCPEK = General P. P. PECKEM
Red 3 lines: RNKO = Lieutenant Colonel KORN
Red triangle: ORR = Lieutenant ORR
Red cross: EERDELD = General DREEDLE
Red diamond: R_EDYOC-LEVE_ = Major - DE COVERLEY (the 'dash' is part of his name)
Red shield: UOSOMD = Colonel MOODUS
Blue star: JMRJRARAOO_O_AMJM = Major MAJOR MAJOR MAJOR
Blue moon: TYALNE = Lieutenant NATELY
Blue teardrop: RFYAA -= Captain AARFY
Blue square: RWNE = Captain WREN
Now, we can work out the 'values' talked about in the question...
If we consult the standard European (because this puzzle is set in Europe) scoring system for Stratego, a General is worth 9, a Colonel 8 (we shall count the Lieutenant Colonel as a Colonel too), a Major 7, a Captain 6, and a Lieutenant 5. Summing the scores for the red team and blue team separately, we get value of RED 46 and BLUE 24.
The square where we will find the 'flag' (another Stratego playing piece, note) is therefore that numbered 22 - the difference between the two teams' scores. Thus we thematically catch the flag in 22 (i.e. the third square in the third row down, marked by a completely blank playing piece)! Very satisfying...
All that remains is to identify the island...
...which must surely be the island setting for this World War II -based novel: Pianosa. After all, the novel's context entirely fits the set-up given for this puzzle (a small island somewhere in Europe, [on which] a battle is fought in the middle of World War I)!
It's worth noting also that the puzzle's instructions have been written in a way that imply that to find the flag you need to find the hidden values, whilst to find the hidden values it might help you to find the flag. This paradox is very reminiscent of the so-called 'logic' at the heart of the 'Catch-22' in the novel, in which the book's fighter pilots will only be excused from flying dangerous missions if they are found to be insane, but any pilot who expresses a concern that they might be insane is thereby showing themselves to be sane by demonstrating a rational concern for their own safety, and thus cannot be exempted from flying! (Yes, it's a head-scratcher...)
