Well, the US Open has played on 3 different surfaces, so there isn't much of continuity as there is in Wimbledon. However, Sampras and Federer have 5 each on hard courts, and Connors has 5 from 3 different surfaces. I'll give the edge to Fed, -- 5 consecutive wins and 100% wins in finals.
1) Federer
2) Sampras (Won in 3 different decades, and as a teen, twenties,
and thirties)
3) Connors