Reports say that someone died during the protest/occupation at the Capital building. Given that, is it reasonable that some of the persons who stormed the building could be successfully prosecuted under federal or D.C. felony murder charges?
Not under federal law, where the enumerated felonies are arson, escape, murder, kidnapping, treason, espionage, sabotage, aggravated sexual abuse or sexual abuse, child abuse, burglary, or robbery. Under DC law, the triggering felony may be
arson...first degree sexual abuse, first degree child sexual abuse, first degree cruelty to children, mayhem, robbery, or kidnaping, or in perpetrating or attempting to perpetrate any housebreaking while armed with or using a dangerous weapon, or in perpetrating or attempting to perpetrate a felony involving a controlled substance
The prosecution would have to prove beyond doubt that the shooter was attempting to commit mayhem (the only crime that is imaginably related to the events). But "mayhem" is different from rioting. The elements of mayhem are set forth in the jury instructions, namely intentionally attempting to cause a permanent disabling injury. When the facts are know, we might be able to assess the credibility of a mayhem charge.
To build up on the the user6726's answer above, if someone in that crowd took the extra steps which caused the police to believe that there was a threat to life (eg, by yelling something threatening like "kill em all"), then they possibly provoked the shooting. The individuals who did provoke it could conceivably be guilty of mayhem. And, therefore, felony-murder rule would apply. They would almost certainly be guilty if it could be shown that they intentionally made the utterance to provoke a heightened police reaction (such as the shooting).
I am not suggesting that anyone in that crowd screamed the phrase "kill em all", by the way. Although I have seen a claim that someone in that crowd was chanting "hang Pence." Since the Vice President was in the building at the time, that could have been the reason for the police's shooting.
Otherwise, this was a clear case of obstruction of justice. Since the stated intent of their actions was obstructing a Congressional procedure.