How can I get an iPhone to play songs in order
Is it possible that you have shuffle enabled? The shuffle button in the playlist list is not a toggle, so that wouldn't tell you. Here's how you can find out:



If the shuffle icon is blue, it means your iPhone is playing on shuffle. 

Something else you could check is if Shake to Shuffle is enabled:



If it is, you could accidentally activate shuffle without knowing it.

Hope this helps.