I was wandering if this is working or not:

If Robert Baratheon is the only King character in play, he gains: 'Any Phase: Kneel Robert Baratheon to play an 'Any Phase' event card from your discard pile as if you just played it from your hand. Then, shuffle that event card back into your deck.'

Missing recruit

Spy in their midst

Beguiled bodyguard

Summer reserves

Winter reserves

All five Reinforcement events are Any phase. Can I use Robert to put these Event/characters into play?

I lose a mil challenge, have Missing recruit in the discard pile. I kneel Robert, put the Missing recruit into play. But after this the Then cannot kick in as the Missing recruit is already a character and not an event.

Yes, when an event card is in play as a character, it is only considered to be a character. So you do not return the character to the deck with Robert's ability.