Although I don't think a word exists in common usage I wouldn't hesitate to use Milleversary.
While The Greek root work kilo- could be used, when it comes to the passage of time, Latin root words are more commonly used.
Mille is the latin word ( and French and Italian spelling ) for 1,000. and we use it with the other popular time-related word: Millennium. We also use the Latin centum for 100 (in century and centennial) rather than the Greek hekaton.
By way of contrast, we use the greek prefixes kilo- and hecto- often in weights and measures.
- A hectare is 100m x 100m
- Kilogram, kilometre, kilopascal
Additionally, we often use Roman numerals to signify or demarcate points in time. M means 1,000 in Roman numerals. You see MCMXVIII all over Europe on monuments erected referring to WWI, like the Welsh National War Memorial which has on it MCMXIV–MCMXVIII on its outer frieze.
You used to see Copyright marks all the time using roman numberals as well, like ©MCMLXXIV (before 2000 mostly, as ©MMI is a little odd-looking I'd imagine).
French still extensively uses Roman numerals to refer to centuries. Xe is often used to mean the 10th century or dixième siècle.
The very passage of time on a clock is STILL very often marked in roman numerals, from I to XII. For these reasons, I'd definitely say milleversary sounds more natural than something like kiloversary if it's anything beyond measuring how many days a bacterial strain has survived inside a petri dish.