You’re eligible for the flu vaccine this year (2019-20) if you’ll be aged 65 or over on 31 March 2020. That is, you were born on or before 31 March 1955.
So if you’re currently 64 but will be 65 on 31 March 2020, you do qualify.
It’s important that you benefit from having the most effective vaccine.
For those aged 65 or over, this is either the adjuvanted trivalent vaccine or the cell-grown quadrivalent vaccine.