There's no such button in Premiere Pro, but there is a shot matching tool in Speedgrade CC:
It's not a hardware-referenced correction so it doesn't actually match 'cameras' - instead it looks at the spectra of each shot and tries to work out the differences between tints on shadows/midtones/highlights. You can't feed it a GoPro sweeping landscape and an Alexa interior headshot, but if the two frames depict roughly the same content it does quite a good job. You can then save the correction data for each camera as a 'look', and back in Premiere Pro CC that look can be applied to all the other bits of footage via the Lumetri effect.
If you want an absolute 'reset' of each clip back to a reference standard, again you'll need to use Speedgrade; this time with the aid of a Macbeth chart. That workflow is a lot more complicated as it was only designed to work with cinema hardware. There is a hacky workaround using Lightroom and the X-Rite plugin:
- Export a still frame showing a Colorchecker card,
- Import to Lightroom as a DNG file,
- Use Lightroom & X-Rite to make a DNG calibration profile,
- 'Develop' the still frame so the chips are now accurate (and set your expoure and luma end points),
- At this point you could save the develop preset and apply it to other video files in Lightroom's Library module but you'd have to transcode your footage and Lr's video export options are limited to say the least.
If you want to use the 'calibration' back in Premiere, it gets fun:
- Send the developed DNG to Photoshop and export as a TARGA file,
- Import the TARGA to Speedgrade CC, then shot-match your video of the Colorchecker to this still frame (here's where you lose a lot of accuracy as the shot matcher isn't comparing each color chip, only the RGB curves),
- Save the correction data as a .look,
- Apply back in Premiere with the Lumetri effect.
I'm very pleased with the results I've been getting using re:Match:
Andrew Devis has a great tutorial:
I use a Nikon D800 and a Sony Z5U, both configured with fairly flat color profiles. RE:Match gets me very close with a single mouse click most of the time.