Hello there,
The flare/slip from 3rd to 4th Gear (or from 4th to 5th gear, it depends) is quite common on this 7at transmission. You will find a lot of posts here and there for different nissan infiniti models that share this transmission. As far as I know, it never put an engine light on the board... And it has nothing to do with the hybrid battery.
Did you get an engine light everytime it slips/flares ?
When you floor down the gas, does it still slips/flares or is only during light pressure ?
Have you an obd tool to see what error codes you get ?
Did you ever drain and fill your transmission ?
Did you get the recall for reprogrammation of the hybrid unit/transmission/ecu ?
There is no more infiniti but there is nissan. Here in France some nissan shops have the infiniti agreement. You should have the same in UK ?
Cheers
Edit : you have a shop in Leeds
https://www.infiniti.com/europe/en-gb/auto-repair.html