Memory Alpha provides vague dates of them all being activated in the 2330s, but is there actually any reference to a more precise age difference between the three brothers in any Trek materials?
This is another of those questions that has most likely not yet had a canonical answer. However, Memory Alpha does have some clues that could be strung together to give an approximate date for at least some of it.
Lore was a Soong-type android constructed by Doctor Noonian Soong and Juliana Soong at the Omicron Theta colony and activated on 9 September, 2335.
Design and construction of Data probably started soon after that, following heated discussions between Julianna and Noonien Soong (alluded to in TNG: Inheritance).
Data was activated some time before the Crystalline Entity attacked Omicron Theta in 2336, so to give a reasonable amount of time for development of Data's positronic net as outlined in "Inheritance", it's best to assume the Entity attacked in late 2336 (mostly taken from here).
She relates to Data that she and Dr. Soong had created and lost three prototypes prior to Lore, and it's generally accepted that B-4 is one of them. Again hypothesising, based on a comparison of Julianna's account of Data's early years, Data's own account of an early dilemma about his own development in TNG: Eye of the Beholder and B-4's shown behaviour, B-4 could be taken to be the third prototype - advanced enough for his positronic net to adapt and evolve.
Since it took around a year to develop Data following Lore's deactivation, and that Data was in fact a step backwards in technical excellence (the famous "I am not less perfect than Lore" concept from Datalore and Family), it might be safe to assume that the gap between B-4 and Lore was a year to two years in length. Which puts B-4's activation somewhere around late 2333 to early 2334.
Happy for others to add more evidence. The many published timelines don't seem to have much information about the Soong androids.