How do I fit Patankar's SIMPLE algorithm to cylindrcal coordinates? What will be the form of flux terms, Jx,Jy and Jz?

I am not sure if you are trying to compare the terms of the N-S eqns one to one as far as the rectangular cartesian and cylindrical co-ordinates are concerned and then looking for the corresponding Jx, Jy, etc. I have the following suggestions :

(a) Derive the N-S eqns yourself for the r-theta-z system. Consult 'Transport Phenomena' by Bird, Stewart and Lightfoot, 'Boundary Layer Theory' by Schlichting and possibly the book on Mechanics by Shames. This will tell you how to prepare the 'mashed potato from dehydrated potato powder' as mentioned by Patankar (Chap.3 p. ~31). (b) Integrate, discretise - you will not have any problem. (c) Be careful about the source term linearisation - read Patankar (Chap 7 : Finishing Touches, p. ~143)- to avoid any pitfall.