Looking back at my book, I'm realizing how flat the dialog is. I'm not known for being funny and I don't consider myself naturally funny, so this is hard for me. How can I make the characters talk to each other in a way that seems natural with bringing in normal humor?
Rather than designing the dialogue, you just need to make sure you have a really good grasp of the different characters - this task isn't really about how funny you consider yourself to be, it's about the characters' personalities.
The dialogue can then be done in a step by step fashion - so something happened, who's going to be first to comment on it, and what sort of thing would they say? And then what would the others be thinking about that, and would they respond?
Interesting dialogue comes from having a mix of different personalities with different viewpoints, kind of bouncing off each other (this is true in real life as well, imagine how boring it would be if everyone thought the same!). So some people will notice the negative aspects of everything while others are positive - some will say the first thing that pops into their head while others will be quieter and think a bit more deeply first, and some will have vivid imaginations and exaggerate things while others are more down to earth. The natural result is interesting dialogue, even if they argue a bit. Your challenge as a writer is not to think up funny phrases per se, but to have characters that think them up for you. That's the only way you can get a naturally flowing interesting dialogue.
It's interesting to note that while the above is true for most literature, in comedy or funny books the characters' personalities tend to be exaggerated to really amp up the differences between them - have a look at your favourite funny book, cartoon or video and you're quite likely to find that (for example) there's one character who's always vividly imagining a huge disaster or dramatic event, countered by another who's always extremely sensible and pragmatic and possibly boring. Either of these wouldn't work as well on their own; it's the combination that does the magic.