After several years with Arsenal Women's youth team, Flannery joined West Ham on 22 July 2022 at aged 16 feeling there was more opportunity for first-team football.

[4] Flannery made her Women's Super League debut for West Ham on 28 September 2022 against Chelsea coming on as an 87th-minute substitute for Lisa Evans in a 3–1 defeat.

[5][1] On 29 January 2023, she provided an assist in the 2–0 win over Wolverhampton Wanderers in the 2022–23 FA Cup,[6] impressing in the West Ham side and being named Player of the Match.

[9][10] In October 2021, Flannery was named in the England under-17 squad for 2022 U-17 Championship qualification fixtures,[11] captaining the team in their opening match defeat against Russia.

[16] Flannery was named as part of the England U19 squad for Algarve Cup fixtures,[17] playing in matches against Portugal, Sweden and the Netherlands in November and December 2023.