burn config file to tinyg board?

You running tinyG or G2core?

No need with tinyG, the controller has onboard EEPROM, configuration changes are persistent.

But since you are asking, likely you are running G2core, where there is no persistent memory (yet).

There are at least 2 options
1. If you are a Chilipeppr user, the SPJS widget has an option to send a set of initialization commands to tinyG(G2core) on startup. Those could be parameter updates.
2. What I prefer to do is rebuild the G2core binary with a custom parameters.h file that has my specific configuration. Those defaults are loaded on restart, can be tweaked from there on.

confusing indeed

So in tinyG FW (and Hardware) space, there is a command, defa=1, that when executed copies the compiled set of defaults into EEPROM, making them current. Used on occasions when EEPROM gets corrupted. The compiled in defaults are almost never what real users want/need.
A few folks have gone to the trouble of compiling their own version of the tinyG FW with their stable machine setting compiled in, so that defa=1 reverts the machine to their native setup.
It is always good to keep a file around on you host computer of all the parameter settings that are working well for you. That would be a $$ parameter dump.