Those are two different, but related, questions?
1) How long does it take light to travel from the core to the surface?
2) Total radiance divided by this time? [Why do you want this one?]
The first is known as the random walk. I think the BA once noted a low estimate of 18,000 years. However, I think this time is based on a simplified model where the Sun's density is held as a constant, which it is not.
The Sun is in a very stable equilibrium with its own gravity. The variation of the total amount of radiation, decade after decade, is only about 0.1%. [UV variance can be as much as 30%, however.]
We know time flies, we just can't see its wings.