Python solution

(throws you an error if you want to rename a file which already exists, e.g. you are processing image 5.jpg while your counter is at 3, but 3.jpg exists already; Could avoid that with a try except clause but then you do not have pictures always incremented by 1 - not sure what you require):

import os
counter = 1
for r, d, f in os.walk(r"Images"):  # can also put a full path here
    for name in f:
        # first argument here is full path to the image
        # second argument is the path + the hex number of the counter + the extension of the file
        os.rename(r + os.sep + name, r + os.sep + hex(counter).lstrip("0x") + os.path.splitext(name)[-1])
        counter += 1

Edit

I further documentated the code, added a status-message and noticed that you want uppercase hex file names:

import os
counter = 1
for r, d, f in os.walk(r"Images"):  # can also put a full path here
    for name in f:
        # full path to original image
        original_fn = r + os.sep + name

        # path + hex number of counter + extension of file
        new_fn = r + os.sep + hex(counter).lstrip("0x").upper() + os.path.splitext(name)[-1]  

        # rename, status print, incrementing counter
        os.rename(original_fn, new_fn)
        print(f"Renamed {original_fn} > {new_fn}")
        counter += 1

Edit 2

Here is a solution to first rename all files to temporary files with random strings attached, and after that rename all of them to hex numbers based on a counter. Hope that solves your problems:

import os
import random
import string

for r, d, f in os.walk(r"Images"):
    for name in f:
        rnd_string = ''.join(random.SystemRandom().choice(string.ascii_letters + string.digits) for _ in range(12))
        original_fn = r + os.sep + name
        new_fn = r + os.sep + rnd_string + name
        os.rename(original_fn, new_fn)
        print(f"Temp. rename {original_fn} > {new_fn}")

counter = 1
for r, d, f in os.walk(r"Images"):  # can also put a full path here
    for name in f:
        original_fn = r + os.sep + name
        new_fn = r + os.sep + hex(counter).lstrip("0x").upper() + os.path.splitext(name)[-1]  
        os.rename(original_fn, new_fn)
        print(f"Final rename {original_fn} > {new_fn}")
        counter += 1

There is below a bash script. Change the values of dest_dir and source_dir

Do not forget to make it executable with chmod +x flattener.sh

#!/bin/env bash

dest_dir="/var/tmp/flat-files"
source_dir="parent-dir"

if [ ! -d "${dest_dir}" ] ; then
  mkdir -p "${dest_dir}"
fi

if [ ! -f "${dest_dir}"/index.dat ] ; then 
  printf "1" > "${dest_dir}"/index.dat || exit 1
fi

find "${source_dir}" -type f -print0 |\
  xargs -0 bash -c ' \
    for filename ; do \
      index=$(cat '"${dest_dir}"'/index.dat) ;\
      printf "%d" $((index+1)) > '"${dest_dir}"'/index.dat ;\
      if [[ "${filename}" =~ [.] ]] ; then \
        extension=."${filename##*.}" ;\
      else \
        extension="" ;\
      fi ;\
      mv -vu "${filename}" '"${dest_dir}"'/$(printf "%X" $index)"${extension}" ;\
    done' flattener

With bash >= 4.0 and cp (no mv/rename):

shopt -s globstar
unset int
for i in **/*.jpg; do
  ((int++))
  printf -v hex '%x' "$int"
  echo cp -v "$i" "FolderAllTogether/${hex^^}.jpg"
done

If output looks okay, remove echo.