Kvachov was a product of the Zorya Luhansk academy and competed with the youth in the Ukrainian Youth Football League.[1][2] He would ultimately graduate to the senior team and secure a contract for the 2014–15 season.[1][3] After failing to appear for Luhansk, he left and was picked up by Veres Rivne in the Ukrainian Second League.[2][4] Though he was signed with Veres, he would finish the campaign with league rivals Enerhiya Nova Kakhovka.[5] In his debut season with Nova, he played in 10 matches.[6] He would return to Nova for the following season and played in 27 matches and recorded 2 goals.[6]
After two seasons in the third division, he would debut in the country's second-tier league for the 2017–18 season by signing with Kremin Kremenchuk.[7] He would leave Kremin after the conclusion of the season to pursue other playing options.[8] Kvachov would remain in the second division the next season by securing a deal with Kobra Kharkiv.[9] The season would become a tumultuous one as he spent the year with three different organizations after Kharkiv experienced financial issues he was transferred to Sumy.[10] Ultimately, he finished the campaign with Bukovyna Chernivtsi in the third division.[11] After the season's conclusion, he left Bukovyna in the summer of 2019.[12]
In 2022, he played abroad in the German circuit with TSV Ziemetshausen.[13] Throughout the season, he would assist the club in avoiding relegation.[14]
Kvachov would further venture abroad this time to the Canadian Soccer League with FC Dynamo Toronto for the 2023 season.[15][16] In his debut season in the Canadian circuit, he helped the club finish fourth in the standings.[17]