As you might know, Keith Richards plays around with a lot of different tunings.
  The version of "Jack Flash" from the Rolling Stones Rock N' Roll Circus album
  is kind of weird.  I don't know if Brian Jones is even playing (He was probably
  stoned out of his mind)  But I hear Keith. This version is kind of interesting.
  The tuning is low to high (E,Bb,E,G#,B,E) or basically an open E chord.
   I don't know if this is the counter melody, but here is the song from that record:


   Main riff

  ---------------------------------------
  --0--0---------------------------------
  --x--x------0-2--5---0--2--5---0-2-5---
  --7--7------0-2--5---0--2--5---0-2-5---
  --7--7------0-2--5---0--2--5---0-2-5---
  --7--7------0-2--5---0--2--5---0-2-5---

  Chorus
  D                      A              E                  B  (Repeat)
  ----------------------------7-7--5----0-----------------------
  ----------------------------5-5--5----0-------------------7---
  -----------------------5-5--5-5--5----0------12--10--12---7---
  10-10--12-12----10-----5-5--5-5--5----0------12--10--12---7---
  10-10--10-10----10-----5-5--5-5--5----0------12--10--12---7---
  10-10--10-10----10-----5-5--5-5--5----0------0---0---0----7---

  Breakdown
  B                     E       D       C#    B   (repeat four times)
  ----------------------------------------------
  ----------------------------------------------
  -7-7-7---7-7-7--------12------10-----9------7-
  -7-7-7---7-7-7--------12------10-----9------7-
  -7-7-7---7-7-7--------12------10-----9------7-
  -7-7-7---7-7-7--------12------10-----9------7-