I agree with the other posters - worth nipping this in the bud swiftly.
Not getting Neil to speak to him is sensible; it'd probably come off as aggressive. Regardless of Neil's diplomacy skills, there'd be fewer hopes of retaining any friendship w/Steve after you'd got a boyfriend to have a few words with him. The friendship you're willing to have with Steve ... may prove insufficient for what he wants, in any case. I question the wisdom in telling Neil but different strokes for different folks! It's feasible you could get Steve to tone it down without making him feel bad. I get the impression he's either lonely as you said or perhaps he's seeing how far he can go? Granted, there is a different between flirting & sharking. I like the keyboard courage phrase above - certainly sounds possible!
If you do particularly want to stay friends with Steve and really do want to say something, take a direct, brief & calm approach.
Bad:
Dear Steve, Lately in your emails I've noticed you stepping over the line between banter and unwelcome attention. Initially I didn't know how to take some of the compliments. Now, I know I don't like some of what I've read. I'm in a relationship and even if I wasn't, it'd never be you. Your personal hygiene alone is a dealbreaker. Don't bother me again. - Kelly 
Slightly better (replying to one of his flirty lines):
Thanks for the compliment. Y'know, maybe I'm getting the wrong signals here and chances are you're just being kind and friendly. All the same with Neil and I working out so well, I'll feel more comfortable if you didn't say that kind've thing. I know you'll understand.
If you're not that bothered whether a friendship continues here or ends because he wanted more, then simply ceasing communication with him might be an easy option.
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