Tricky. I looked at it as follows:
Need a player from each of ZIM/BAN/AFG to make up 11 - I think that has to be Flower/Shakib/Rashid as they're the only truly world class players from those nations. That means two spinner slots and a middle order keeper batsman are locked in.
Then you've got to have Bradman - can't ignore a guy averaging 100. So that's number 3 locked.
That leaves you IND/WI/ENG/NZ/PAK/SL/SA to make up (ideally) two openers, three fast bowlers, a seam bowling all rounder and a middle order batsman. Seam bowling all rounder and openers are the hardest positions to fill there IMO, so I'm going to pick the best players in those categories first and go from there. Best openers from those countries statistically are Gavaskar and Cook so they're in - also like the combination of skill in all conditions. Seam bowling all rounder (given ENG are out) then has to be Kallis. That leaves three fast bowlers to pick from PAK/WI/NZ/SL - SL not famous for their fast bowlers, so I'll pick the best from each of PAK/WI and NZ - in my eyes Akram, Marshall and Hadlee. This leaves a middle order batsman from SL, which has to be Sangakkara.
My team is therefore:
1. Gavaskar (IND)
2. Cook (ENG)
3. Bradman (AUS)
4. Sangakkara (SL)
5. Kallis (SA)
6. Flower (WK) (ZIM)
7. Shakib (BAN)
8. Hadlee (NZ)
9. Rashid Khan (AFG)
10. Akram (PAK)
11. Marshall (WI)
Pretty happy with that - specialist openers, bats to 11, two good spinners, a frightening opening combo in Akram and Marshall (left and right arm), very handy seam support from Hadlee (and Kallis).
For a series on the subcontinent with proper turning pitches I'd swap Sangakkara for Murali and Hadlee for Williamson - so the side would be:
1. Gavaskar
2. Cook
3. Bradman
4. Kallis
5. Williamson
6. Flower (WK)
7. Shakib
8. Rashid
9. Akram
10. Marshall
11. Muralitharan