Here's the situation, party consists of:

Marines Militant Tactical (Ultramarine variant)

Dark Angel Tactical

Screaming Gecko Librarian (frontal assault focused chapter)

Grey Phoenix Assault (Imperial Fist successor)

Wrath of Corax Assault (Ravenguard successor)

They are investigating some corrupted servitors when they are ambushed. A tough fight, ends in twelve rounds with the assault marines, librarian and Militant holding their own and taking down the corrupted servitors. The Dark Angel missed every single time. He had to be bailed out by the Militant and the Phoenix, who took down all their attackers and had to chop down the ones on the Dark Angel. The Dark Angel has demanded he do penance for failing so spectacularly (he had a 58% of hitting in melee after aiming). This was a bad run of luck, but in game he would be devastated at such a display of incompetence. I just can't think of how a Dark Angel would punish himself for this.

Certainly it would seem the Marine is out of favour with the Emperor.

He has obviously been slacking in his devotions, and must pray harder.

Few ideas you could do. First one is is to start the next missions some wounds down to represent the self flagulation, or take less requisition next time, leaving their chapter trappings behind.

Isn't self flagellation more of an Imperial Fist's thing? I think that the dark angel would probably seclude himself while not on mission and devote himself to praying, at least until he proves himself worthy in battle again, which would result in a minor cohesion penalty.

To me this sounds more or less entirely as something that should be an RP thing with little or no rule-mechanical parts to is. If you let him RP it out I would think that it will come out better that way and the player, if he's interested of course, will have a chance to get to do something more with his character than just walking around and shooting stuff. And since he outright asked for penance I would think that he's more into RP:ing it rather than just getting a few marks for the next mission. But I could be wrong of course.

The self punishing is more a Fists & successors thing. With a Dark Angel, the mindset is more tainted with suspicion and paranoia. He might be trying to work out why he missed so often. He KNOWS he's that good. He fought combat servitors in the training cages for decades. He's fought any number of more skilled, more vaunted opponents and emerged victorius. So why has he failed now? What is different? Was he targeted by something, by someone? Who was behind this? Have his 'brothers' some form of complex about the fact that they are mere successor chapters and that he's a member of Legion One? Have they been sabotaging his efforts? Maybe the Deathwatch is as slack at background checks as the Dark Angels believe and one of his 'brothers' is actually a member of the fallen, attempting to undermine his confidence, weaken him so they can start whispering their lies in his ears...

If the character is prone to paranoia or is starting to walk the road of the Primarch's Curse, maybe a dificulty penalty on Cohesion checks for the next mission as he attempts to work out who he can trust.

Possibly (if if works for your campaign) you can reward the poor luck with a storyline - someone WAS sabotaging him. But whom?! Dun dun DAH!

yes, gurkh and the professor have given you my only good replies: seems to me the Dark Angel will seclude himself for penance-prayers and introspection (and possibly some vigorously vicious training), warmly fueled by paranoia and possible suspicion...which may or may not be true...and, yeah, probly best to try to keep it in the 'roleplaying' arena, and outside of actual 'rules' (though i also like the idea of not bearing chapter relics/gear until atoned for...)