would it be good if TDecompressionStream could handle this header?
No, because this is a different header. Other than different header, ZLIB has also Adler32 checksum at the end, while GZIP uses CRC32.
TDecompressionStream is for ZLIB stream, but you can skip the header and decompress pure deflated data.
Would it be good if this stuff was documented in the unit? Or somewhere?
I dont know, maybe it could be explained better somewhere. I am not entitled to write FPC documentation.
Documentation states
"If ASkipHeader is true, then the gzip data header is skipped"
That is not true, what is skipped is ZLIB header.
If its feasible I would suggest you using pure deflated data without any headers. Then in FPC use TDecompressionStream with SkipHeaders - its the same as you would just do "inflate".