Help with Tikz graphic

The following uses the shapes.symbols library to get the signal node shape which is what you're looking for to get the right look for Hospital Staff etc.

I also changed their positioning (using the node (a) to get the height right) and changed your arrows to get what you want.

documentclass[border={2pt 2pt 2pt 2pt}]{standalone}
usepackage{tikz}
usetikzlibrary{arrows,positioning} 
usetikzlibrary{shapes.geometric,shapes.arrows,shapes.symbols,positioning}

begin{document}
begin{tikzpicture}[fill=red!20, in arrows/.style={signal, signal to=east, text width = 1.5cm, minimum height=2baselineskip, align=center}]
%draw[step=0.5cm,color=gray] (-15,-15) grid (15,15);
draw[thick, fill=blue!25] (-5,-5) -- (-5,7) -- (7,7) -- (7,-5)-- (-5,-5);
draw[thick, fill=red!25] (-4.8,-1) -- (-4.8,6.8) -- (6.8,6.8) -- (6.8,1)-- (3,1) -- (3,-1) -- (-4.8,-1);
draw[thick, fill=yellow!25] (-4.8,-1.2) -- (3.2,-1.2) -- (3.2,0.8) -- (6.8,0.8)-- (6.8,-4.8) -- (-4.8,-4.8) -- (-4.8,-1.2);

path 
(0,.5) node(a) [fill=white,ellipse,draw,align=center]{ Milling & Meeting Area}
(-2.5,-2.5) node(b) [fill=white,rectangle,rotate=0,draw,align=center] { BeveragePantry}
(0.5,-2.5) node(c)  [fill=white,rectangle,rotate=0,draw,align=center] { Offices}
(3.5,-2.5) node(d)  [fill=white,rectangle,rotate=0,draw,align=center] { QuietRoom}
(0,-3) node(e)  [rotate=0,align=center] { Secure Rooms}
(-3,-6) node(f) [draw, arrow box, arrow box arrows={north:.5cm}] { Volunteers}
(0,-6) node(g) [draw, arrow box, arrow box arrows={north:.5cm}] { Chaplains}
(3,-6) node(h)  [draw, arrow box, arrow box arrows={north:.5cm,south:.5cm}] { Visiting on  Wards}
(a)++(-5.5,0) node(j)  [draw, anchor=east, in arrows] {Hospital Staff}
(j.east)++(0,1) node(i)  [draw, anchor=east, in arrows] { Visitors}
(j.east)++(0,-1) node(k) [draw, anchor=east, in arrows] { Patients}
(-3.1,3.5) node(l) [fill=white,rectangle,rotate=0,draw,align=center] { Hindu & Sikh Prayer Room}
(-.5,3.5) node(m) [fill=white,rectangle,rotate=0,draw,align=center] { New St Luke'sChapel}
(2,3.5) node(n) [fill=white,rectangle,rotate=0,draw,align=center] { Main PublicSpace}
(5,3.5) node(o) [fill=white,rectangle,rotate=0,draw,align=center] { Muslim PrayerRooms &Washing Facilities}
(5,-1) node(p)  [fill=white,rectangle,rotate=0,draw,align=center] {MDT Room}
 (1,6) node(q)  [rotate=0,align=center] {Large Open 24 hours a day}
;


        
draw[black,triangle 45-triangle 45] (a) -- (b);
draw[black,triangle 45-triangle 45] (a) -- (c);
draw[black,triangle 45-triangle 45] (b) -- (c);
draw[black,triangle 45-triangle 45] (a) -- (d);
draw[black,triangle 45-triangle 45] (l) -- (a);
draw[black,triangle 45-triangle 45] (m) -- (a);
draw[black,triangle 45-triangle 45] (n) -- (a);
draw[black,triangle 45-triangle 45] (o) -- (a);
draw[black,triangle 45-triangle 45] (p) -- (o);
draw[black,triangle 45-triangle 45] (o) -- (a);
draw[black,triangle 45-triangle 45] (p) -- (o);

draw[black, triangle 45-triangle 45] (i) -- ++(3,0) coordinate(tmp) |- (k);
draw[black, triangle 45-triangle 45] (j) -- (j-|tmp) -- (a);



draw[thick] (-4.8,-1.2) -- (3.2,-1.2) -- (3.2,0.8) -- (6.8,0.8)-- (6.8,-4.8) -- (-4.8,-4.8) -- (-4.8,-1.2);


end{tikzpicture}


end{document}

A code variant which uses styles for the basically same nodes with different text, foreach for the repetitive task of drawing all those arrows, and cycle where applicable.

documentclass[border={2pt 2pt 2pt 2pt}]{standalone}
usepackage{tikz}
usetikzlibrary{arrows} 
usetikzlibrary{shapes.geometric,shapes.arrows,shapes.symbols}

begin{document}
begin{tikzpicture}[
    fill=red!20,
    in arrows/.style={draw, signal, signal to=east, text width = 1.5cm, minimum height=2baselineskip, align=center},
    boxes/.style={fill=white, rectangle, draw, align=center},
    arrowboxes/.style={draw, arrow box, arrow box arrows={#1}}
  ]
%draw[step=0.5cm,color=gray] (-15,-15) grid (15,15);
draw[thick, fill=blue!25] (-5,-5) -- (-5,7) -- (7,7) -- (7,-5)-- cycle;
draw[thick, fill=red!25] (-4.8,-1) -- (-4.8,6.8) -- (6.8,6.8) -- (6.8,1)-- (3,1) -- (3,-1) -- cycle;
draw[thick, fill=yellow!25] (-4.8,-1.2) -- (3.2,-1.2) -- (3.2,0.8) -- (6.8,0.8)-- (6.8,-4.8) -- (-4.8,-4.8) -- cycle;

path 
(0,.5) node(a) [fill=white,ellipse,draw,align=center]{ Milling & Meeting Area}
(-2.5,-2.5) node(b) [boxes] { BeveragePantry}
(0.5,-2.5) node(c)  [boxes] { Offices}
(3.5,-2.5) node(d)  [boxes] { QuietRoom}
(0,-3) node(e)  [align=center] { Secure Rooms}
(-3,-6) node(f) [arrowboxes={north:.5cm}] { Volunteers}
(0,-6) node(g) [arrowboxes={north:.5cm}] { Chaplains}
(3,-6) node(h)  [arrowboxes={north:.5cm,south:.5cm}] { Visiting on  Wards}
(a)++(-5.5,0) node(j)  [anchor=east, in arrows] {Hospital Staff}
(j.east)++(0,1) node(i)  [anchor=east, in arrows] { Visitors}
(j.east)++(0,-1) node(k) [anchor=east, in arrows] { Patients}
(-3.1,3.5) node(l) [boxes] { Hindu & Sikh Prayer Room}
(-.5,3.5) node(m) [boxes] { New St Luke'sChapel}
(2,3.5) node(n) [boxes] { Main PublicSpace}
(5,3.5) node(o) [boxes] { Muslim PrayerRooms &Washing Facilities}
(5,-1) node(p)  [boxes] {MDT Room}
(1,6) node(q) {Large Open 24 hours a day}
;


foreachx in {b,c,d,l,m,n,o}
  draw[black,triangle 45-triangle 45] (a) -- (x);
draw[black,triangle 45-triangle 45] (b) -- (c);
draw[black,triangle 45-triangle 45] (p) -- (o);

draw[black, triangle 45-triangle 45] (i) -- ++(3,0) coordinate(tmp) |- (k);
draw[black, triangle 45-triangle 45] (j) -- (j-|tmp) -- (a);



draw[thick] (-4.8,-1.2) -- (3.2,-1.2) -- (3.2,0.8) -- (6.8,0.8)-- (6.8,-4.8) -- (-4.8,-4.8) -- cycle;


end{tikzpicture}


end{document}