Designing a 8 bit ALU
What you show is similar to the old AMD 2901 4-bit "bit-slice" ALU chip. You should be able to cascade them to any length, but longer equals slower because of the carry chain. You will need an AND gate to combine the "zero" flags. You can take the "carry", "sign" and "overflow" flags from the most-significant chip.

To cascade them, you simply need to tie the "carry-out" of the lesser significant 4 bits to the "carry-in" of the next higher 4 bits. Be sure to tie the lowest order "carry-in" to something you can control (one of your instruction bits) because it needs to be a 0 for an ADD, and a 1 for an INCREMENT or a SUBTRACT.

Wikipedia link: https://en.wikipedia.org/wiki/AMD_Am2900