What an interesting thought. I never compared Bible flipping with witchcraft or sorcery or new age thinking for that matter. I don't think that applies very well in this case. Yet, I admit, to pray each time and anticipate that if you drop your Bible, or expect an "answer" to your prayer may be haphazard to say the least.
The best way to interpret life is with Scripture, and the best way to understand Scripture is to study it correctly with respect and of greatest reverence. I would compare your Bible flipping as equivalent to "casting lots" as they did in Acts (1:26). This is the last recorded event that they casted lots. Why? We don't know except soon after Pentecost came.
It's as if the Holy Spirit became the counselor, guide, and comforter (John 16:4-11) that Jesus said would happen.
In proper interpretation of the Word there are always two understandings to be observed: What was the writer's intent as directed by God, and what is God saying to me today through His Word. In many cases the first is easier to find than the last because in the latter we might be trying to find God's specific will for our life or circumstances.
So, can God use Bible flipping? Why not? But why did He not use casting lots, or why didn't Christians (Paul, Timothy, Silas, Peter, and the rest )rely upon casting lots again? I believe it's because they had the Holy Spirit. We do too, and along with Him we have the complete Word of God at our disposal.
Is Bible flipping or dropping witchcraft, I think not. But is treating God's Word in a rather disrespectful way or by "chance" responsible, I would say no to that choice either. Personally, I have found that God meets us where we are, and He has even used just "opening the Bible" to guide me. But usually, the passage had a direct relation and context to my circumstances. In other words, I might have read Joshua 1:8-9 when I was fearful over a challenge. And so God was tellling me "Don't be afraid." I knew God was speaking that day. Just this week I was reading Ps 27, and 25, a key message that kept popping out was "Wait on the Lord." I got the hint, God is telling me to be patient with what I am praying over.
There are a couple of other resources that are wonderful in helping with this. One book is called Reading the Bible for All It's Worth (can't remember the author). And another one is, Hearing God's Voice by Henry Blackaby.
The best way to seek God's answer after a time of prayer is to review and know God's Word about that specific issue. If that doesn't address it, then pay close attention to what God is having you read through now i.e. Psalms, Matthew, or whatever book you are reading through. Watch your circumstances, listen to the Holy Spirit, speak to good Christian friends whom you respect, and trust that God will do as He said "You will seek me and find me, when you seek me with all your heart," Jeremiah 29:13. So, here, and in other places God promises that His Will can and will be found by those who seek Him. He'll make sure of that.
Hope this isn't too long. Besides, you wouldn't drop a road map hoping that you'd discover the right way to get to where you needed to go. Course, God can use anything He chooses, even Bible flipping from time to time.
Daniel...wayoverbogey