Is there a way to see the amp levels while charging my iPhone?

I don't believe so.

The available API for battery state in iOS gives you only 5% resolution. It might be possible to write an app that polls battery state and calculates a rate of charge based on the time between 5% intervals but I don't know of any apps that do this. If you want to get your app on the app store that's about the best way of measuring it directly. I know of an app that captures the screen and looks at the battery charge image to determine charge an alternative way but that's iffy, the size or appearance of the battery indicator might change between versions and then it breaks.

Jailbroken devices are a whole other can of worms. I know how to get 1% resolution on devices with a private API but you can't get such an app on the store so distribution is going to be limited.

BTW your terminology is a bit confusing. "Current" would be the right term, less commonly "amperage". I had to read a couple of times through to work it out, I thought you were talking about music volume at first.

I cannot speak for official apps, but I know that for jailbroken iDevices, there is a console/Terminal command that can be run called powerlog that provides live feedback about power usage, (dis)charging levels, amperage/current, capacity, etc. It's a very powerful tool, and if you already have a jailbroken device and are comfortable with using command-line tools (a big if, I suppose :P), then it is definitely an option to consider.