Born in Trento, Trentino, Fiamozzi started his playing career at Varese. After Varese failed to win promotion to Serie A, Torino signed Fiamozzi in June 2012 for €370,000 and sold striker Osarimen Ebagua back to Varese for €470,000.[1] He was immediately loaned back to Varese by Torino for the 2012–13 Serie B season. That year, he made his first team debut for Varese, playing in the Coppa Italia, as well as making 14 appearances for the senior team during the season.
In June 2013, Varese bought back Fiamozzi in a co-ownership deal from Torino.[2] He scored his first goal in Serie B during Varese-Pescara, 3–2.[3] On 21 June 2014, Torino's 50% share of Fiamozzi was redeemed by Varese.[4]
Lecce
On 25 July 2018, Fiamozzi signed a three-year contract with Serie B side Lecce.[5]
Empoli
On 10 January 2020 he was loaned to Empoli for a two-year term with a purchase option.[6]