Vlantis started football at the age of 13, when he enlisted in the infrastructure departments of
AEK Athens. On 13 December 1976 he signed a professional contract and was promoted to the men's team. Vlantis made his debut on 6 March 1977, in a 1–1 away draw against
Panserraikos. He was member of the team that reached the
semi-finals of the
UEFA Cup, despite not making any appearance in the tournament. In general, during his first three seasons at the club, Vlantis didn't manage to make many appearances, due to their star roster at the time and his simultaneous engagement with his studies at the
National Technical University of Athens, from which he graduated with a degree in
Civil engineering. Nevertheless, he was part of the squad that won the domestic double in 1978 and the
Championship in 1979. In the summer of 1979 the need to continue his studies at the Polytechnic School of the
University of Patras, forced him to move to
Patras and join
Panachaiki as a loan. In order to stay in the city for another year, he was loaned to APS Patrai for the following season. After the end of his loan spells at Patras in the summer of 1981, he was again loaned to
Diagoras. Vlantis returned to AEK in the summer of 1982, but again was not able to establish himself in the main squad. However, despite having a not so impressive career at the yellow-blacks , he was fortunate enough to be a member of the team at during their peak moments of that era. During the years of his temporary absence, when he was out on loan, AEK abstained from titles and upon his return to the team, they won the
Greek Cup in 1983. His last match with AEK was on 26 June 1983, in a 4–2 win over
PAS Giannina at
Nea Filadelfia. On 28 July 1983 Vlantis was transferred to the second division side
Acharnaikos. The following season he signed for
Atromitos, where he played for 5 seasons before ending his career in 1989. ==Personal life==