After putting eight unanswered goals past Liechtenstein and Armenia in its opening two games under Flick, Die Mannschaft kept up their positive start in Reykjavik.
Serge Gnabry's tap-in and Antonio Rudiger's header had Germany two goals ahead inside 24 minutes and Leroy Sane killed off the contest early in the second half.
Germany passed up a number of further opportunities before Timo Werner added a late fourth to seal a win that moves his side four points clear of second-place Armenia, who were held to a surprise 1-1 draw by Liechtenstein earlier on Wednesday.
Gnabry opened the scoring after six minutes in the 6-0 win over Armenia three days ago and needed just four minutes to get off the mark against Iceland at Laugardalsvollur.
Joshua Kimmich played in Sane with a pass on the spin and the Bayern Munich winger laid the ball on a plate for club-mate Gnabry to convert from close range.
That goal was allowed to stand after a VAR check for offside and the visitors had a second when Rudiger powerfully headed Kimmich's delivery away from Hannes Halldorsson.
Germany was then given a scare when, moments after Werner missed a one-on-one, Johann Berg Gudmundsson struck the post and Albert Gudmundsson's follow-up was ruled out for offside.
Kai Havertz, brought on for Gnabry at half-time, was next to miss a glorious chance as he slotted wide with just Halldorsson to beat, but Sane thumped a third into the rood of the net to seal the points.
After Leon Goretzka had a goal ruled out for offside it was left to Werner to complete the rout, the Chelsea attacker's shot trickling over the line as he made amends for an earlier horror miss from six yards out.