The first thing you should do is ask Apple. An Apple employee at an Apple store may be able to retrieve your photos depending on how damaged the iPhone is. But if your iPhone doesn't turn on, Apple isn't likely to be much help.
You might even be told by Apple that it's impossible to retrieve your photos if your iPhone doesn't turn on, but there are still other avenues to explore.
If your iPhone doesn't turn on, your best bet for retrieving photos that aren't backed up to the cloud is to contact third-party tech repair shops to see if they can help.
It should go without saying that you should look for a trusted and reputable tech repair shop. A good criteria to look for is whether or not the repair shop charges you if the repair or retrieval is unsuccessful.
Jones says she charges $300 for photo recovery, but only if she's able to retrieve the photos. If not, you don't pay.
During your search, you'll likely run into "authorized" Apple repair shops, which are third-party shops supported by Apple. As they're Apple-supported, authorized repair shops will likely tell you the same thing that Apple tells you.