BotRK's Notes section states that the active doesn't actually "steal" movement speed; instead it simultaneously slows the victim by 25%, while giving the user 25% increased MS, stacking additively with other percentage MS buffs. Assuming Chilling Smite behaves in the same manner, the user would get 45% increased MS (25% from BotRK, 20% from Chilling Smite), whilst the victim would suffer a 32% slow, due to how slow stacking works.
However, the formula shown here seems to imply that percentage MS buffs stack multiplicatively with each other, rather than additively. This means the combined MS buff from BotRK and Chilling Smite would come out to 50%, though when you factor in the soft caps applied to total movement speed the difference ends up being negligible. Slow percentage on the victim would remain the same.