Flohr dominated many tournaments of the pre-World War II years, and by the late 1930s was considered a contender for the World Championship.

However, his patient, positional style was overtaken by the sharper, more tactical methods of the younger Soviet echelon after World War II.

He and his brother were orphaned during World War I when their parents were killed in a massacre, and they fled to the newly formed nation of Czechoslovakia.

Flohr settled in Prague, gradually acquiring a reputation as a skilled chess player by playing for stakes in the city's many cafés.

During 1924, he participated in simultaneous exhibitions by Richard Réti and Rudolf Spielmann, and he was still giving displays well into his seventies.

Notable victories were at Bad Sliač in 1932, where he shared first place with Milan Vidmar; Scheveningen in 1933; Bad Liebenwerda in 1934 with 9½/11; Barcelona in 1935 where he tied for first with George Koltanowski; Moscow 1935 where he tied for first place with future World Champion Mikhail Botvinnik; Poděbrady in 1936 with the score of +10 −1 =6; and Kemeri in 1937 where he shared the top spot with Vladimir Petrov and Samuel Reshevsky.

However, with World War II looming, it proved impossible for Flohr to raise the stake money in Czechoslovakia, so the plans were dropped.

AVRO may have been the only time in chess history when the top eight players in the world contested an important tournament.

While AVRO was a strong tournament and Flohr's last-placed finish was no disgrace, his result may also be explained by his difficult personal circumstances at the time.

The German invasion of Czechoslovakia in 1938 had left Flohr, as a Polish-Ukrainian Jew, in grave personal danger.

[2] Flohr did not play in any official strong Soviet events from 1940–42, though he did lose a 1942 match to Vladimir Makogonov in Baku by 2–0.

As the Soviet Union first stopped then reversed the Axis invasion, some chess activity started up again, and in 1943 Flohr won a small but strong tournament in Baku.

His tournament record was impressive, with his tactical skill and excellent endgame technique securing him many famous victories.

He became a much more cautious player in his post-war games and earned a drawish reputation, with many short draws which were hardly contested.

Players such as Vasily Smyslov, David Bronstein, Isaac Boleslavsky, Paul Keres, Alexander Kotov, Tigran Petrosian, Efim Geller, Mark Taimanov, Yuri Averbakh, Boris Spassky, Mikhail Tal, Viktor Korchnoi, and Leonid Stein dominated the landscape with their sharper styles and innovative openings.

According to the site Chessmetrics.com, which compares historical ratings, Flohr was among the world's top 20 players from 1930 to 1951, except for the war years 1942–44 when he was largely inactive; and his ranking peaked at No.