Love these questions.
1998 would be the answer. DT Leonta Rheams went in the 4th round to the Patriots and C Ben Fricke went to the Giants in the 7th.
1990 was next with DT Alfred Oglesby and DT Craig Veasy going in the 3rd to Miami and Pittsburgh respectively while T Joey Banes went to the Oilers in the 11th.
1977 saw DT Wilson Whitley drafted in the 1st by the Bengals and G Val Beecher drafted in the 3rd by Dallas.
1967 had DE Carl Cunningham going in the 4th to the Broncos, DT Paul Otis going in the 9th to the Steelers, and T Charles Fowler going in the12th to the Browns.
50s get harder to tell as guys played both ways and there were 30 rounds in the draft, but we had at least two linemen drafted in 1953, '54, '56, '57, and '58.