This is a difficult one, as going back in time we don't have very reliable data for the balls faced by individual batsmen. The closest I can find to the sort of thing you're talking about was achieved by Pakistan's
Taufeeq Umar, in the second Test against Australia
at Sharjah in 2002-03 - he was out second ball for 0 in the first innings, and was run out without facing in the second. There are ten known cases of "king pairs" - dismissed first ball in both innings - in Tests: by William Attewell (England v Australia, Sydney, 1891-92), Bert Vogler (South Africa v Australia, Sydney, 1910-11), Tommy Ward (SA v Aust, Old Trafford, 1912), Colin Wesley (SA v Eng, Trent Bridge, 1960), Bhagwat Chandrasekhar (India v Aust, Melbourne, 1977-78), Gary Troup (New Zealand v India, Wellington, 1980-81), Dave Richardson (SA v Pakistan, Johannesburg, 1994-95), Adam Huckle (Zimbabwe v Pakistan, 1997-98), Ajit Agarkar (India v Australia, Melbourne, 1999-2000), and Adam Gilchrist (Aust v India, Kolkata, 2000-01).