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You actually put the functions Delta, rho2, and Sigma in the metric at the beginning. You should use them in a closed form as in the following code. Please try this (but first check if the metric is correct).

(If it succeeds, then you can substitute the actual functions in the results):

reset()
M = Manifold(4, 'M', latex_name=r'\mathcal{M}', structure='Lorentzian')
BL.<t,r,th,ph> = M.chart(r"t r th:(0,pi):\theta ph:(0,2*pi):\phi")

var('m a H E')

g = M.metric()

rho2=function('rho2')(r,th)
Delta=function('Delta')(r)
Sigma=function('Sigma')(th)

g[0,0] = -(Delta - a^2*sin(th)^2*Sigma)/rho2
g[0,3] = -(a*sin(th)^2)*((r^2 + a^2)*Sigma - Delta)/(rho2*E)
g[1,1], g[2,2] = rho2/Delta, rho2/Sigma
g[3,3] = (sin(th)^2/(rho2*E))*((r^2 + a^2)^2*Sigma - Delta*a^2*sin(th)^2)
show(g.display())

Riem = g.riemann()
R_up = Riem.up(g)
R_down = Riem.down(g)

Kretschmann_scalar = R_up['^{abcd}']*R_down['_{abcd}']
Kretschmann_scalar.display()