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I did not find any rescaling option, but you can normalize your vector field as follows:

sage: f(x,y) = (x^2-1)*(y^2-1)*x*y
sage: g(x,y) = (x^2+(y-3/8)^2-1/64)*(x^2+(y+3/8)^2-1/64)
sage: plot_vector_field((f(x,y)/sqrt(f(x,y)^2+g(x,y)^2), g(x,y)/sqrt(f(x,y)^2+g(x,y)^2)), (x, -1,1), (y, -1,1))

Which indeed shows sinks, sources, and saddles much better than

sage: plot_vector_field((f(x,y),g(x,y)), (x, -1,1), (y, -1,1))

I did not find any rescaling option, option in the source code, but you can normalize your vector field as follows:

sage: f(x,y) = (x^2-1)*(y^2-1)*x*y
sage: g(x,y) = (x^2+(y-3/8)^2-1/64)*(x^2+(y+3/8)^2-1/64)
sage: plot_vector_field((f(x,y)/sqrt(f(x,y)^2+g(x,y)^2), g(x,y)/sqrt(f(x,y)^2+g(x,y)^2)), (x, -1,1), (y, -1,1))

Which indeed shows sinks, sources, and saddles much better than

sage: plot_vector_field((f(x,y),g(x,y)), (x, -1,1), (y, -1,1))