On your iPhone there is the option to record video in slo-mo. This will be perfectly good for recording your swing.
In terms of other equipment, with a bit of fiddling you should be able to position your phone on your bag to keep it in place. Or you can get a cheap mini flexible tripod with an iPhone holder off of eBay. Something like this: (I don't have this exact one so can't recommend it) You can then easily attach this to your bag.
I prefer the option of the cheap tripod. That way there is no danger of your iPhone slipping down the club dividers and ending up in the bottom of your bag, which as we golfers know is a complete pain!!
