which version is latest battery firmware with the new .701 Spark firmware?

There is no new battery firmware with the .701 Spark firmware.

ok
and which version should be the latest?

If the battery firmware need to update, your app will remind you.

Version 01.00.00.75 is the latest battery firmware.

DJI Elektra ... i didnt get a Update message for the battery, but i have Version .75

Jo__McFly Posted at 2017-11-1 00:50
DJI Elektra ... i didnt get a Update message for the battery, but i have Version .75

You battery is in the latest firmware.  Did you update your firmware of AC? If not, you need to update to V 01.00.0700.

my AC Firmware is .0701

Now things are getting interesting. Look what I have just discovered in post no. 7# in this discussion (second screenshot): https://forum.dji.com/thread-117962-1-1.html

Here the full screenshot:

Hey DJI! Whats Uuup?
i can see .80 for battery ?!?

In the quickly withdrawn Version .700 there was a battery update. In the replacement .701 the battery update disappeared.

Martin Lines Posted at 2017-11-1 01:26
In the quickly withdrawn Version .700 there was a battery update. In the replacement .701 the battery update disappeared.

Thank you for the clarification. Occasionally DJI shows a certain talent for creating confusion...
DJI, please do not take this as an offense, we like you nevertheless!

perhaps the .80 Users got now the hidden 20 minutes flight time