Mfcttrf

documentclass[12pt,reqno,a4paper]amsart
usepackageextsizes
usepackageblindtext
textheight 9.3in textwidth 6.5in
calclayout
usepackagemathtools
usepackageamsmath,amsthm,amsfonts,amssymb 
usepackagehyperref
usepackagemathrsfs
usepackage[all]xy
usepackage[normalem]ulem 
usepackagetikz-cd
usepackage[utf8]inputenc
usepackage[english]babel 
usepackagecolor
pagestylemyheadings
begindocument

begintikzcd
 A arrow[dd, "p"'] arrow[ddrr, phantom, "Rightarrow"] arrow[rr, "q"] & & B arrow[dd, "r"] \
 & & \
 C arrow[rr, "s"] & & D
 endtikzcd

 begintikzcd
A arrow[dd, "p"'] arrow[rrdd, "q"] & & \
& & \
B arrow[rr, "r"] & & C 
endtikzcd

 enddocument

This is what I have written to get a commutative diagram.

I want to add an arrow (Rightarrow) inside the diagram from bottom left corner to top right corner. Can some one help me to do this? I have tried to add using "phantom" but it is not coming as I expected. I want this pointing from top left corner to bottom right corner (or bottom left corner to top right corner).

You can use a phantom arrow, with the label in the middle via description and sloped.

documentclass[12pt,reqno,a4paper]amsart
usepackagetikz-cd

begindocument

begintikzcd[sep=huge]
A arrow[dr,phantom,"to" description, sloped]
 arrow[d, "p"'] arrow[r, "q"] & B arrow[d, "r"] \
C arrow[r, "s"] & D
endtikzcd

enddocument

Why not simply this, to specify the diagram commutes? Unrelated: I took the liberty to simplify your code, in particular removing unnecessary packages (already loaded by another package).

documentclass[12pt,reqno,a4paper]amsart
usepackageextsizes
usepackageblindtext
textheight 9.3in textwidth 6.5in
calclayout
usepackagemathtools
usepackageamsthm,amssymb
usepackagehyperref
usepackagemathrsfs
usepackage[all]xy
usepackage[normalem]ulem
usepackagetikz-cd
usepackage[utf8]inputenc
usepackage[english]babel
pagestylemyheadings

begindocument

begintikzcd[row sep = large, column sep = large]
 A arrow[d, "p"'] arrow[r, "q"] & B arrow[d, "r"] \
 C arrow[ur, phantom, "scalebox1.5$circlearrowleft$" description]arrow[r, "s"] & D
 endtikzcd

 enddocument 

You can shorten a Rightarrow as you like.

For the triangle, you can name the label and draw an arrow to it.

documentclass[12pt,reqno,a4paper]amsart
usepackagetikz-cd
tikzcdsetrow sep/normal=50pt, column sep/normal=50pt

begindocument

begintikzcd
 Aarrow[d, "p"']arrow[Rightarrow, shorten >=25pt, shorten <=25pt, dr]arrow[r, "q"] & Barrow[d, "r"]\
 Carrow[r, "s", swap] & D
endtikzcd

begintikzcd
 Aarrow[d, "p"']arrow[r, "q"] & Barrow[d, "r"]\
 Carrow[r, "s", swap]arrow[Rightarrow, shorten >=25pt, shorten <=25pt, ur] & D
endtikzcd

begintikzcd
 Aarrow[d, "p"']arrow[rd, "q"name=M] \
 Barrow[r, "r", swap]arrow[Rightarrow, shorten >=10pt, shorten <=10pt, to=M] & C
endtikzcd

enddocument

documentclass[12pt,reqno,a4paper]amsart
usepackageextsizes
usepackageblindtext
textheight 9.3in textwidth 6.5in
calclayout
usepackagemathtools
usepackageamsmath,amsthm,amsfonts,amssymb 
usepackagehyperref
usepackagemathrsfs
usepackage[all]xy
usepackage[normalem]ulem 
usepackagetikz-cd
usepackage[utf8]inputenc
usepackage[english]babel 
usepackagecolor
pagestylemyheadings
begindocument


begintikzcd
A arrow[dd, "p"'] 
arrow[rr, "q"] & & B arrow[dd, "r"] \
& & \
C arrow[rr, "s"] arrow[uurr, phantom, "scalebox2$Rightarrow$" description, sloped] & & D
endtikzcd.

 enddocument

Here there is two version using xy package. The first has the classic tips,

documentclass[a4paper,12pt]article
usepackage[all]xy
usepackageamssymb
newcommandRLongrightarrowrotatebox45$Longrightarrow$
usepackagegraphicx
begindocument
xymatrix@R=3pc@C=3pcRLongrightarrow
A ar[d] ar[r] & B ar[d] \
C ar[r] & D
enddocument

the second has the same tips of tikz-cd. See the code below and the image:

documentclass[a4paper,12pt]article
usepackage[all,cmtip]xy
usepackageamssymb
newcommandRLongrightarrowrotatebox45$Longrightarrow$
usepackagegraphicx
begindocument
xymatrix@R=3pc@C=3pcRLongrightarrow
A ar[d] ar[r] & B ar[d] \
C ar[r] & D
enddocument