How to find out the used code?
Your original sample is too small to know if it's FLAC or not.  You need a long sample, and then look for 0xff 0xf8 bytes in it to see if you have FLAC block headers.  Your additional sample from the beginning of the streadm is definitely FLAC.

FLAC is a complex format for compressing audio (format overview), with many variations on sample size and so on.  It's binary, and resyncable, which means that periodically there is some known marker.

FLAC streams will begin with a FLAC header (starting with 66 4C 61 43, which is fLaC in ASCII), and have a FLAC block header at least every few thousand bytes, these headers begin with ff f8).
Good general overview at Wikipedia article. 

Your original stream

Your stream is given as "ASCII with hexadecimal escapes", as might be used in many programming languages, including C, Python, PHP.

x\xdam\xdd]\xc4\xeemZ\xc7q)2\xcc\xd6cL\x1a1\x8c\xc9hc\x0c)\xeb^\xaf\xd7Z


As it's just binary, your stream is better represented as:

78 da 6d dd 5d c4 ee 6d  5a c7 71 29 32 cc d6 63
4c 1a 31 8c c9 68 63 0c  29 eb 5e af d7 5a 0a


(Easily seen in almost any Linux shell with echo -e "x\xdam\xdd]\xc4\xeemZ\xc7q)2\xcc\xd6cL\x1a1\x8c\xc9hc\x0c)\xeb^\xaf\xd7Z" | hd)

Assuming your stream actually is FLAC, you will need a larger sample to decode it, as you are missing the header information.  Without the header or block header information, it's impossible to reliably tell all the compression details.

Your longer sample

Your longer sample from the beginning of the stream is definitely FLAC.  You can see this because it begins with 'fLaC' and is decodable by the program metaflac, part of the open-source program flac (download page).

We see this by putting your sample in a file (as binary) and then running metaflac to see if it can decode it.  It can.  The following is in a Linux shell:

# create SAMPLE file with echo -e or python or whatever
$ metaflac --list SAMPLE
METADATA block #0
  type: 0 (STREAMINFO)
  is last: false
  length: 34
  minimum blocksize: 4096 samples
  maximum blocksize: 4096 samples
  minimum framesize: 1013 bytes
  maximum framesize: 2009 bytes
  sample_rate: 48000 Hz
  channels: 1
  bits-per-sample: 16
  total samples: 239616
  MD5 signature: 095b92012ab7f2b5a0b75473897bce8a
METADATA block #1
  type: 4 (VORBIS_COMMENT)
  is last: true
  length: 40
  vendor string: reference libFLAC 1.3.2 20170101
  comments: 0


FLAC details

If you want to examine by hand (just to see if you have FLAC), you can use the definition and look for sync flags on the blocks.

A Sony sample file is 24-bit, 96 kHz sampling rate, and has portions which look like this:

00060099: ff f8 3b 1c 00 2c 10 0d e0 e0 a1 23 e5 a6 64 a2
00063511: ff f8 3b 1c 01 2b 14 ff ff eb 00 02 38 0f 20 0c
00067822: ff f8 3b 1c 02 22 14 fb 7b 42 fb 57 cd 0b 4c c6
00072135: ff f8 3b 1c 03 25 14 f4 3c b9 f3 e0 98 03 01 0d
00076338: ff f8 3b 1c 04 30 14 12 cf 29 12 b5 16 0b 2c ac


These are found just by looking for the sync pattern ff f8 in the file, and displaying 16 bytes from there: this is how we find block headers. 

The beginning of the header is:

/-----ff------\ /------f8-----\ /-----3b------\ /-----1c------\
1_1_1_1 1_1_1_1 1_1_1_1 1_0_0_0 0_0_1_1 1_0_1_1 0_0_0_1 1_1_0_0
1 1 1 1 1 1 1 1 1 1 1 1 1 0                                     sync flag
                            0                                   filler
                              0                                 filler
                                0 0 1 1                         1152 samples
                                        1 0 1 1                 96 kHz
                                                0 0 0 1         mono
                                                        1 1 0   24 bit/sample
                                                              0 filler


This is followed by the increasing block numbers 00, 01, 02, and the other portions of the header.  (Note that the block numbers are coded in a non-obvious way for blocks above 127, but with a recognisable pattern.)

Not every sequence beginning fff8 will be a block header, as some might be data.  You have to check other details in the block header to be certain it is a header and not data.  But what I've shown here is enough to show it's almost certainly a FLAC stream.

From the format definition https://xiph.org/flac/format.html


  Since a decoder may start decoding in the middle of a stream, there must be a method to determine the start of a frame. A 14-bit sync code begins each frame. The sync code will not appear anywhere else in the frame header. However, since it may appear in the subframes, the decoder has two other ways of ensuring a correct sync. The first is to check that the rest of the frame header contains no invalid data. Even this is not foolproof since valid header patterns can still occur within the subframes. The decoder's final check is to generate an 8-bit CRC of the frame header and compare this to the CRC stored at the end of the frame header.
  
  Again, since a decoder may start decoding at an arbitrary frame in the stream, each frame header must contain some basic information about the stream because the decoder may not have access to the STREAMINFO metadata block at the start of the stream. This information includes sample rate, bits per sample, number of channels, etc.


The FLAC reference continues with the exact details of all the bits, which was used to give the example above.

Fully decoding a stream

In the first instance, use the open source program flac to see what you have.  On this little sample, the program reports FLAC__STREAM_DECODER_ERROR_STATUS_LOST_SYNC (which is what we would expect for a small chunk from the middle of a stream.)

Once you have something you can make sense of, you can use the open source library libFLAC to do what you need.