The unsatisfying short answer first:

To my knowledge NO current mobile phone uses a real strobe flash.

Why is that?

The problem with strobes and electronic shutter as employed in a mobile phone is, that the a "real" flash from a conventional flash bulb is really really really short.

This creates problems when you read out the sensor in a line-by-line fashion, as most sensors do. You have to make sure that you read all your sensor lines within the short timeframe of the flash of light. Otherwise you will get uneven lighting or even a half lit frame.

To overcome this, you can use techniques like high speed sync, where you simply prolong the flash by pulsing multiple flashes or by using a global shutter, where you read out all lines of the sensor at the same time.

A far easier solution is, to not use a flash bulb, but another source of concentrated light: a high yield LED. And that is the cheapest and most practical solution.

Regarding the power of the flash: As with all integrated flash lights, you have to make a compromise between some specifications:

• Brighter is usually bigger. This means the light itself and the heat sinks to cool it.
• Brighter usually means more power drain. So how much of you battery may the thing use?
• Light is becoming weaker over distance by inverse square law. So adding more reach quickly becomes a real challenge, given the space constraints and energy available.

But why do you want to have a conventional flash?

I assume you associate a flash bulb with a light of higher intensity. And that is true for most conventional flashes. A flash emits a lot of light and heat during a very small time period.

Given the small light source and the placement near the lens, the real use of this as a means to create acceptable images is very limited.

As the camera in the phone is tailored to constant light, your best option, if you wanted to light bigger spaces, would be to invest into constant lights like Photo LED lamps and light-formers to shape the light to your needs. The results will be looking way more professional than a built-in flash of any strength in your mobile phone ever could.