Fire propagation simulator
Matlab, 235 257 190 182 178 bytes

Input: Matrix A, 1x2 vector p containing the starting coordinates.

function t=F(A,p)
[n,m]=size(A);x=2:n*m;x(mod(x,n)==1)=0;B=diag(x,1)+diag(n+1:n*m,n);k=sub2ind([n m],p(1),p(2));t=max(distances(digraph(bsxfun(@times,((B+B')~=0),A(:))'),k))+A(k)


Explanation:

Instead of simulating the the fire propagation, we can also understand this as a "find the longest shortest path" problem. The matrix is converted into a weighted directed graph. The weights of the paths to a single node correspond to the time to burn said node. E.g. for a matrix

5   7   7   10
5   2   2   10
4   5   2   6


we get the connected graph:



Where node 1 is the upper left matrix element and node 12 the lower right element. Given starting coordinates p, the shortest path to all other nodes is calculated. Then the length of the longest path of those shortest paths + the time to burn the initial node equals to the time to burn the whole matrix.

Ungolfed and commented version with sample starting values:

% some starting point
p = [3 2];
% some random 5x6 starting map, integers between 1:10
A = randi(10,5,6); 

function t=F(A,p)
% dimensions of A
[n,m] = size(A);
% create adjacency matrix
x=2:n*m;
x(mod(x,n)==1)=0;
B = diag(x,1)+diag(n+1:n*m,n);
B = B+B';
B = bsxfun(@times,(B~=0),A(:))';
% make graph object with it
G = digraph(B);
% starting node
k = sub2ind([n m], p(1), p(2));
% calculate the shortest distance to all nodes from starting point
d = distances(G,k);
% the largest smallest distance will burn down last. Add burntime of initial point
t = max(d)+A(k);