Avraham was born on March 6,1917 in Sopron, Hungary. He was born when his parents, Hannah née Blumschein and Yosef Fleischman, were older, and he was a brother to Magda, Yitzhak and Yaakov. The family was traditional but secular. The father of the family was an administrative director of the courts in Sopron, while the mother was a seamstress. The sons were Zionist, Beitar members; the daughter was a Communist. She reached the rank of lieutenant colonel in Communist Hungary. His brother Yitzhak perished in the Holocaust.
Due to an antisemitic incident, the father was fired. As a result, Avraham had to go out to work (in a clothing store) once he had completed eight years of study.
He participated in the Aliyah Bet program on Naomi Julia in September 19,1939. He was arrested in Sarafand for a while, and once he was released, he joined Beitar, first in Rosh Pina, then in Nes Ziona. He then moved on to Beer Tuvia, and he worked in the construction of the British Army base in Nahal Sorek. He was recruited to Lehi by Eliyahu Giladi with another three friends. The British arrested one of them, and due to the concern that he was also wanted, Avraham moved to Tel Aviv. As it turned out, the British arrested another person with the name of Avraham Fleischman, which saved him.
He started working in restaurants, eventually becoming a cook; this allowed him to provide food for escapees and fugitives. He lived in an apartment on Geula Street where HeHazit and various posters were printed. There was also a cache of arms and a cache of “confiscated” diamonds.
Avraham took part on the attack on the parking lot of the “Kalaniot,” the destruction of warplanes at Kfar Syrkin, confiscating weapons at Tel Litwinsky, and more. During the attack on the railway workshops, Avraham was the commander of the mine-laying unit. In the getaway vehicle, he was second from the end. The first was killed by gunfire, and Avraham’s hand was hit, but he jumped into a ditch and was among the few to escape. He received first aid in Kfar Hasidim and eventually made his way to Ramat Gan.
In early 1948, Avraham joined the nascent military, joining the valley battalion and taking a squad commanders’ course. As the IDF was established, he joined the Givati Brigade. He was demobilized after the War of Independence.
On December 30,1946, he married Aviva Gold, who was a witness in the Eichmann trial and wrote the book The March about the Holocaust. They had a son, Gidon, in 1952, and later a grandson Shai and granddaughter Hen.
Avraham began working as a cook. He opened a restaurant with a partner, but it failed and he worked at Oron as a cook from 1954 to 1958, then at Kargal as a kitchen manager, until he retired in 1985. After, he volunteered in Beit Yair two or three times a week.
He passed away on November 9,1998.