This is easy in AVX with the VBROADCASTS command, or in SSE if the value were doubles or floats.
How do I broadcast a single 8-bit value to every slot in an XMM register in Delphi ASM?
You mean you have a byte in the LSB of an XMM register and want to duplicate it across all lanes of that register? I don't know Delphi's inline assembly syntax, but in Intel/MASM syntax it could be done something like this:
punpcklbw xmm0,xmm0 ; xxxxxxxxABCDEFGH -> xxxxxxxxEEFFGGHH
punpcklwd xmm0,xmm0 ; xxxxxxxxEEFFGGHH -> xxxxxxxxGGGGHHHH
punpckldq xmm0,xmm0 ; xxxxxxxxGGGGHHHH -> xxxxxxxxHHHHHHHH
punpcklqdq xmm0,xmm0 ; xxxxxxxxHHHHHHHH -> HHHHHHHHHHHHHHHH