The 21-year-old is Spurs’ first signing in the January transfer window.
Fraser Forster has played 10 consecutive games, of which only two were won by Tottenham, after Guglielmo Vicario broke his ankle in a 4-0 win over Manchester City in November, but illness forced Brandon Austin to recover from defeat to Newcastle on Saturday.
Vicar is expected to return as very soon until the end of February.
Kinsky, who is a U21 International Czech Republic, has made 29 appearances for Slavia this season.
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