It's obviously too unproductive and wearisome to hold the phone over the book in one hand for hours, as I read and flip pages with the other hand.
Your question includes a solution too, and that is the wrong solution.
Using the phone's light as a reading light is definitely an unfortunate idea in the long run, because it will enforce faster discharge of the battery, followed by other charges. That is exactly what kills phone batteries.
It is a lot more recommended to buy some cheap appliance, designed to do exactly that task. These appliances can be head (your own :)) mounted, wall mounted, free standing on a table, even attachable with a (big) clip to the book. They might provide both battery-stored energy, as well as connection to the wall socket (possibly through an adapter).
Just throw a search on your preferred search engine, and choose from the large variety something that suits your needs best.
For the love of god, buy a lamp! A little table lamp or perhaps a standard lamp, depending on where you're reading. Or else if there's some special need for darkness, look into buying a torch, many are rechargable.
You can even get, quite inexpensively, the sort of lamp cave explorers use. Straps to your forehead. The better ones are rechargable, the cheaper ones aren't. Although you could get rechargable batteries and a charger to counter that, since this is something you're going to use a lot you don't want to shell out for endless batteries.
A phone is not designed to make a good lamp Using it's camera flash LED gets hot and eats battery massively. They're useful in emergencies cos you've always got your phone on you, but it's not an everyday sort of thing.
You can get a clip-on gooseneck mount for a cell phone or tablet that could be used to hold your phone in an appropriate position. I picked up one of these cheap one Black Friday and was very impressed with how well it holds my tablet. There are other models that have larger clamps, cup-holder mounts, etc.
That said, if you're talking about using the camera flash LED as a light then I'd definitely discourage that -- it'll kill your battery, and those things get mighty hot. If you're just talking about using your phone's screen then it's better, but I'd still just buy a small lamp.
Pictures 1 and 3 already display a solution for this: the glass or cup can double as a standard for your phone. Presumably you don't need the light while you're drinking. Since those objects are round, balancing your phone might be a bit of a problem. Otherwise, you might be better off with basically any rectangular paperweight. Maybe other books which are still on your 'to read' list? (I tend to keep those on a bookcase shelf separate from the ones I already read, but this might be another way to set them apart.)
You can purchase Head Mount for the phone, e.g. this one looks nice.
This way just attach the phone over your forehead, turn the light on, and you can read freely, anywhere, with both hands free.
Happy reading! :-)