It's definitely a tricky sentence to parse, and the speaker is trying to phrase it in a clever way, so let's break it down into pieces.
Since 「うのぼれ」 means "pride," "conceit," or "vanity," this part would translate as "He doesn't know conceit," with the implication being that he has no conceited thoughts. In other words, he's a humble person.
The ending 「男はいない」means "there is no man/person," and 「男」 is being modified with
「彼ほどうぬぼれを知らない」. So this section means "There is no man who doesn't know conceit as much as he does not know conceit," which smooths out to "There is no man less conceited than him."
And now we modify the above statement with 「ぼくが知る限る」, meaning, "as far as I know." So the whole thing translates to "As far as I know, there is no man with less idea of conceit as him." Smooth that out a bit and add some dramatic flare, and you can say
"As to conceit, he is the farthest from it of any man I know." Basically, the speaker is saying that the person is not at all conceited, though personally I'd have gone with a les flowery translation, like "I don't know any man as humble as he is."
「What I understand is: As far as I know, there isn't a man who doesn't know how conceited he is.」
I think there are two things that might have tripped you up here, and both have to do with ほど. Yes, ほど sometimes translates as "how," since it shows an extent. But the extent that ほど shows is determined by the word that comes directly before it.
So 「彼ほど〜」 doesn't mean 「he is so 〜」, it means 「to the extent that he is/does」. With 「彼ほどうぬぼれを知らない」, ほど is telling us 「not knowing conceit as much as he does not know it」, or 「being as non-conceited/humble as him」
If you DID want to say 「As far as I know, there isn't a man who doesn't know how conceited he is.」, then you wouldn't use ほど, but instead use a different word, like どれだけ or どれほど.
In simplified terms, ほど means "to the same extent as," so it has to be comparing like to like.
Taro is humble, and you want to talk about whether or not someone else is as humble/humble to the same extent as Taro? Then you'll use ほど.
But on the other hand, if you just want to say "how humble Taro is," in the sense of "People should appreciate how humble Taro is" or "Nobody notices how humble Taro is," then you wouldn't use ほど, but instead どれだけ or どれほど.