Which loudspeaker output on the amplifier should the BluBOX be connected to?
The BluBOX does not represent a load resistance, nor does it convert anything. The signal is looped through directly from the SPEAKER LEVEL INPUT to the THRU. In particular, this means that the load resistance that is connected to the THRU must match the impedance that the amp needs.
In other words: if an 8 ohm cabinet (or a load box) is attached to the THRU of the BluBOX, the BluBOX must be connected to the 8 ohm output of the amp. If there is a 16 ohm cab (or cabinet combination) attached, the BluBOX should be connected to the 16 ohm output of the amplifier, etc.
Life hack - only for AMP1
If there is an 8 ohm speaker connected to the 8 ohm output of the AMP1 (e.g. NanoCab or FatCab), you can also use the 16 ohm output of the AMP1 to connect the BluBOX. In this case, please make sure that you plug a dummy plug (open ends, no short circuit) into the THRU socket of the BluBOX, which suggests to the BluBOX that a speaker is connected (why you should do this, you can find out here).
If there is no speaker connected to the AMP1, it doesn't matter to which SPEAKER OUT you connect the BluBOX.
You can find all of the connection options for the BluBOX here: What connection options are there for the BluBOX?