Richard didn't kill them: he had no need to "get rid" of them as Titulus Regius declared them illegitimate; and should he have killed them/Buckingham killed them/they died of sickness, there was no benefit to their deaths unless he displayed the bodies to prove they were dead and not a focus for rebellion.
Buckingham didn't kill them as he joined Morton and Marg Beaufort's rebellion on the understanding that it was to address the grievances against the boys - and possibly allow him a chance at the throne himself - but very quickly became Marg Beaufort's coup to install her son as the next possible king.
Marg Beaufort didn't kill them as a) she had no chance b) she adored her son too much to keep him fretting all his life about whether they were still alive. He was her precious first-born and he was always looking over his shoulder worrying about whether the princes would turn up. She would have told him to set his mind and throne at rest. Hence Tudor is also not a suspect.
It seems fairly obvious to me that the boys were not killed. That the older boy appears to have died - none of the pretenders ever claimed to be Edward the older boy. There is a tradition at Gipping Hall in Suffolk (family home of the Tyrrell family) that the boys were sent to live there with their mother once she came out of sanctuary in March 1484. Personally I think the younger boy was probably Richard the younger prince. William Stanley who had supported Tudor, his brother's step-son, at Bosworth, supported Perkin Warbeck in 1495 (ie thought he was one of the boys) and was executed for it. The boys' mother Elizabeth Woodville was deprived of her livings and placed in a convent at the time of the Lambert Simnel conspiracy, a conspiracy that her surviving first-born son Dorset supported.
Perkin Warbeck was at times called "the Duke of York" by Henry Tudor, and once executed, was severly beaten about the face so that he could not be recognised.
It gained Richard nothing to get rid of the boys, and everything to hide them away (possibly abroad eventually) and keep people guessing. Both he and other members of the family were quite devout and at no point were any masses ever designated for the memory of the boys. Josephine Wilkinson's recent book on the princes is rather good, as is Audrey Williamson's somewhat dated 1978 book The Mystery of the Princes.