I've just noticed this behavior today trying to import image too big for the 16MB flash onboard of RB952Ui-5AC2ND. ROS has pop out the error message complaining on insufficient disk space and aborted import, but almost all of a flash is still occupied. You can even upload 19.2 MB file to it, though flash size is 16MB !!! Of course, after device reboot, the file magically disappear, but the space occupied is the same (see image attached).
Reboot does not help, nor version upgrade, nor reinstalling ROS over Netinstall. I've tried ver. 6.48.6 and 6.49.5, same thing.
So, considering this as a BUG, some fix should be a priority.

Generally ROS devices with tiny flash storage (16MB) and at least decent amount of RAM (64MB or more) will have RAM disk as root of file storage ... actual flash storage will appear under /file flash. And your hAP ac lite is a good example of such devices.

Now you know that your 19 MB file was placed to RAM disk you can (hopefully) understand why it disappeared at reboot ... because RAM disk gets wiped with rebooting. And you can verify that by comparing RAM usage with and without that large file.

The other issue you've got is that you're uploading ROS for wrong architecture (x86 versus mipsbe) and with ungodly old version (6.38 ... current v6 long-term is 6.48.6). I'll assume you did it to illustrate the point of being able to upload large files.

But the real problem you have is that flash storage has only 3.1MiB free. Normally this should be enough to perform upgrade. You did not mention your current ROS version, some recent v6 versions have some problems with flash space which prevent them from being upgraded ... and the only sure way out of it is to netinstall the device. Prior to doing it, backup configuration, save it off device ... after netinstall, you can restore configuration from that backup. If upgrading to v7, procedure technically works but there have been reports of unstable behaviour which was cured by factory reset and manual reconfiguration afterwards.

Thanks for this extended clarification, but I think you've mised my point here. On the left part of the picture,you can see there is no file under 'flash' root,and still there is over 12MB of 'something' in there. This state of flash was direct result of my unsuccsesful image import into metarouter. That's the only thing you haven't discuss in your post... Having in mind the title of my post, can someone tell me how can I free up the flash on my device, excluding actions I've already tried (read above).

That 12MB of something is installed RouterOS, it takes roughly that much.

I have not had time to dig more into it, but it seems that Sob is right. What confused me was, that after the very first boot with original factory ROS (the device is new) , that window on the picture attached showed almost all of 16MB free, then I tried to import image, but at the same time I did upgrade online. And suddenly those 12MB of "something" appeared. I am not 100% sure in this, but in the old version consumed flash amount was not reported correctly, but now it is.
So, I must withdraw my bug report. It's a pity though, for designers made gave this device MetaRouter feature but practically unusable, and yet there is RB750gr3 ...

MetaRouter is dead anyway, v7 doesn't have it anymore, there will be containers instead (not yet, but in some future version). And while there won't be much joy with 16MB flash either, there's better chance to squeeze in something small. With MR it was pretty much impossible.