Is there an app for iPhone or iPad that will let me record log color space video? It seems like with such an abundance of instagram-ish "filter" apps, developers probably have access to raw sensor data. Are there any apps designed to record it in a flat color profile for postproduction grading?
This announcement article dated January 11, 2017 indicates that there will be an upgrade to the app FiLMiC Pro which may accommodate what you are looking for. Note that the FiLMic Pro App Store web page indicates the latest release is 12/23/2016 - I do not know when the update the article speaks of will be available:
The forthcoming update will introduce a new log mode that allows filmmakers to shoot videos with a flat picture profile containing additional stops of dynamic range.
Of note, they have apparently released a beta version for testing and demo of the LOG capture. Compare in particular the dark area of the dashboard in the lower left hand corner in this example of source video vs. the same footage after grading with BlackMagic Design's DaVinci Resolve. Disclaimer - these videos are from the article and the quality of the color grading vs youtube compression and such is relative. Also, as an example of the extra detail shooting this way may afford, note in the third shot, the shadow detail of the hat before and after.
Likely you don't need this information, but here is a recent article which provides a decent overview of what it means to shoot in log color space , or, record a "flat color profile." Also, some related VideoSE Q&A about shooting considerations.
The iPhone display and camera are already in logarithmic color spaces. I think you are asking about linear color space.
I very much doubt that Apple allows direct access to the camera hardware. I haven't seen any apps that required it.
But even if you somehow could, you'd find that the conversion to sRGB/BT.709 is done in the camera hardware, as is the compression. And even if you could access the raw sensor, you'd find the data noisy and unwieldy.
So, no. Sorry.
True Log recording is not possible in iOS till date. There is no access to raw sensor data when it comes to shooting video on iOS. RAW is possible only when you click a picture, not video. I hope iPhone was fast enough to process 30 RAW pictures per second but right now it can't handle more than 3 per second. I hope iOS 12.0 offers developers better access to the sensor to shoot real LOG videos, i.e. when developers can apply gamma curve of their choice when A2D conversion takes place in Bayer array filter.