No live vaccine is used in the flu vaccine so you can't get the flu from it. (Sometimes people are already exposed to somebody with the flu virus without knowing around same time as the vaccine, people are infective from 24 to 48 hours prior displaying flu symptoms )
However because your immune system is compromised it might not be as effective. Ask your oncologist about timing to have it. Have family around you have it. Herd immunity is very helpful.
https://www.cdc.gov/flu/protect/keyfacts.htm