Born in Budapest, Filkor started playing football with local side MTK, before joining Maltese club Pièta Hotspurs on 22 August 2006 on free transfer. Before he moved to Malta, Internazionale had contacted MTK for a possible transfer of Filkor in July 2006. As Pièta Hotspurs ranked category 3 in FIFA training compensation distribution scheme, Hotspurs supposed to pay MTK €70,000 and if Internazionale signed directly, it supposed to pay MTK €160,000 as training compensation. MTK alleged that the transfer to Malta was the plan of Inter to save cost on training compensation regulated by FIFA.
Internazionale
On 25 August 2006, he was transferred to Internazionale for €90,000, where he played in their youth team. During the season, he made also his first-team debut in a 2006–07 Coppa Italia game against Messina, on 9 November 2006. However, failing to get much playing time, in January 2008 he was loaned out to Serie B side Grosseto in order to gain some first team experience. During his six months at Grosseto, Filkor won a total of 14 first team appearances, but only four of them as a starter. For the 2008–09 season, Inter loaned Filkor out again, this time to Sassuolo, a newly promoted Serie B team. He made a total of 15 league in one season and a half spent at the club, before leaving for Gallipoli, on another loan spell, for the remainder of the 2009–10 season. On 30 July 2009, the Court of Arbitration for Sport ordered Inter to pay MTK €144,000 for training compensation.
Milan
In July 2010, he completed a move to crosstown rivals A.C. Milan, along with fellow Internazionale players Cristian Daminuţă and Marco Fossati for a combined fee of €7 million. However, soon thereafter, he was loaned to Serie B side Triestina for the season. In July 2011 he was loaned out again to Livorno, another Serie B club. The following season, he was sent on a third straight loan spell in Serie B, this time at Bari. However, during the January transfer window he was called back and loaned to Pro Vercelli. For 2013–14 season he moved to France, joining Ligue 2 side Châteaurouxon loan. On 1 September 2014 he was signed by Avellino.
Filkor was called up for the Hungary national football team in 2007. He was on the bench against Canada, in a match between the two sides on 15 November 2006. He made his international début on the pitch on 7 February 2007 in the last 5 minutes of a 2–0 win against Latvia in a friendly. He has also captained the Hungarian U-19 side.
