A good question... and one that required a bit of researching on my part. In short, the birth of the Chaos Dwarfs pre-dates the Time of Three Emperors by
thousands of years.
From the Dwarfs 8th edition army book:
View attachment 85702
The number on the right relates to the Imperial Calendar (ignore date on the left as that is based on the Dwarf calendar). The Chaos Dwarfs are essentially "born" when they first start worshipping Hashut. So based on this text we know for certain that the Chaos Dwarfs exist in the year -3900.
The 8th edition Empire book provides us with the timeframe for the Time of Three Emperors:
Which starts in 1547
View attachment 85703
And ends in 2303 (when Magnus the Pious unites the Empire)
View attachment 85704
So the Chaos Dwarfs exist by the year -3900 and the Time of Three Emperors doesn't start until 1547. So the Chaos Dwarfs have been around for 5447 years when Time of Three Emperors begins!