After reading your responses in your thread, it seemed to me that you were kind of "hoping" to find a phone. The phone would be the last straw you needed to really break things off - once and for all. So, I read your profile and then read your journal (which you suggested people do to get your "full story"), to get a broader perspective.
After reading everything, I can see how hurtful this has all been to you during the first year of your marriage. Your H sounds very immature and has very poor boundaries, to say the least. He seems to have no idea how much pain he has caused you. He just seems to do whatever his childish mind wants to do at the time. He doesn't sound like a great H, I'm sorry to say.
I don't have any big ideas for you, but here are a few thoughts:
1. It seems like you already know the answer to the equation you are trying to solve. You're just trying to prove how you got the answer. You'd like something more solid, in terms of proof, before you make any final decisions. I can see why you feel this way, although the answer already does seem very apparent. (Are you prepared financially and emotionally for what you are probably going to find? Do you have a plan, because you're probably going to need one.) With that said, here are some thoughts on getting what you're looking for.
2. "Ithoughtiknewya" has a good idea about getting a Voice Activated Recorder. This should accomplish the same thing as finding the phone...and more. If you find the phone, you still don't know what he is saying on the phone. With a VAR you do.
3. Brkn_heartd also has a good idea about a key logger.
4. In terms of finding the actual phone, Brandon's idea is clever.
5. after installing the var and keylogger, I would also suggest providing him with plenty of open space opportunity. Take the kids for play dates with friends. Visit a relative some weekend without your h, etc.
6. During this time of "additional discovery" you need to be relaxed and casual and not show any suspicion.
Flirting during a marriage is bad news, IMO. For your situation the news is obviously much worse. Unfortunately, your H is more than a flirt. He is being inappropriately sexual with other women. Whether he has slept with one of them yet is still unknown, but he probably has (business trip...bringing something to her room at night) there is no question that he will do that in the future, just IMO.
I don't know how to end this post, other than to wish you luck. With a VAR and keylogger in place, I'm sure you're going to all the proof you need to justify the answer that already seems apparent. Good luck.