How to scale output of butterfly unit radix 2 for further stages?
Obviously if you multiply two 8-bit numbers and then want the result to fit in 8 bits you will loose some precision.

You need to make a decision regarding how much error you are willing to accumulate in each stage.  If you are not willing to have any error then you will need to increase the number of bits in each stage.

When doing fixed point arithmetic like this its often useful to interpret the vectors as scaled integers.  For signed numbers you could use the following scale...

1000_0000... = -1.00...
0000_0000... =  0.00...
0111_1111... =  0.99...

The multiplication of two N-bit signed vectors results in a vector that is 2*N - 1 bits long.  When using scaled integers you would then just take the upper N bits of the result to get back to your original scale.