Jews were worried with the rise of Hitler and the Nazis, but they had no idea of the genocide that was to come was even possible. The thought of murder of millions of people wouldn't seem feasible.

Please keep in mind that there had been a history of antisemitism in the public sphere of Germany before the rise of Hitler. After the Germans won the Franco-Prussian War in 1870, many influential public figures spoke against the Jews for not identifying with the nationalist identity of Germany. While many Germans thought they Jews as their own separate group, many were still friends with members of the Jewish community. Germans supported Hitler because he was anti-communist, represented the old Germany, and he focused on putting people back to work. While the rise of Hitler and the Nazi's to power certainly scared Jews, most thought it wasn't enough of a threat to flee their homes and immobile family. Many believed that everything would go back to normal, they fought for Germany or their fathers fought for Germany, and that they were true Germans at heart. To answer your question though, about 1/3 of all Jews in Germany fled the country after Hitler began ramping up antisemitic laws:

After Hitler rose to power, the appearance of the Aryan paragraph in the Third Reich in 1933 began the institutionalized discrimination of Jews by forbidding them from being in office or becoming professors at universities. Now the Jews begin to worry but nothing too drastic happens in the following couple years, mainly due to the 1936 Olympics and Hitler not wanting to draw to much attention to the treatment of Jews in Germany. After the Olympics, Hitler stepped up anti-Jewish propaganda and pushed legislation that boycotted Jewish businesses. Then the mistreatment of Jews continue gradually; all Jewish men must take middle name Isaac, German government decides to put large J on jewish passports, no jewish doctor can treat aryan patients, no jewish lawyer can represent aryan clients, all jew business men forced to have aryan partners and sell their business to the aryan partners, jewish students are expelled from school, all by the end of the 1930s.

The turning point that made Jews realize that they were in grave danger in Germany was Kristallnacht, or "The Night of Broken Glass" where Jewish synagogues and businesses were destroyed, there was a ferocious onslaught of jews, every synagogue was burned, and 300 jews were killed. After this event is when you start seeing mass fleeing of Jews from Germany.

One of the best accounts of life as a Jew (in fact he was a protestant convertite, but that mattered little to the Nazis) in Germany during WWII is the diary of Victor Klemperer, professor of Romanistics in Dresden before forced out of his job, stripped of his titels, who only survived because of his aryan wife, chronicling how the other jews of his community get deported, killed, terrorized and murderd (in the end, there were about 70 jews left in Dresden). It's a haunting and pretty unique story. His diary chronicles the life under daily tyranny, and, as a philologist, he makes many interesting remarks on the use of language by the National Socialists, which are compiled in the Lingua Tertii Imperii, the 'language of the third Reich', a worthwile read in itself.

There is an english translation available in three volumes, though the last one is concerned with life in the soviet occupation zone and the fledgling GDR.