The only signs of contact in the show, you have already marked from In The Beginning. There is no other tie-in material that concentrates on Dukhat's life, or this period.
Given that one special prequel movie is all we can draw from, the only signs point to the Vorlons making contact just before the Earth-Minbari War.
In the prequel movie In the Beginning, one of the scenes is of Delenn questioning a series of workers who are bringing alternate atmospheric equipment aboard the Grey Council ship. This naturally begs the question, what is aboard that could require such equipment. She is halted in her questioning by Dukhat, who only admits that there is a secret being kept. This would have to coincide roughly with when the Vorlons came on board.
We cannot say with any certainty how long they were in contact with Dukhat before that. Given that their... "physical" appearance ... would likely have been required to be convincing, I believe it's safe to say they had only recently made contact. Bringing their atmosphere aboard suggests creating a permanent space for them, making them comfortable, so recent wouldn't have been that same day or hour. Of course, on that same voyage, Dukhat died, so how much and how long they were actually able to advise him is an open question.
