Since it looks like you want to combine multiple files, I guess that I would regard this as a legitimate usage of cat:
cat /home/FileSystemCorruptionTest/*.chk | while read -r line do echo "$line" done > /home/FileSystemCorruptionTest/`date +%Y_%m_%d_%H_%M_%S`_1.log
Note that I moved the redirect out of the loop, to prevent overwriting the file once per line.
Also note that your example could easily be written as:
cat /home/FileSystemCorruptionTest/*.chk > /home/FileSystemCorruptionTest/`date +%Y_%m_%d_%H_%M_%S`_1.log
If you only actually have one file (and want to store it inside a variable), then you can use <<< after the loop:
while read -r line do echo "$line" done <<<"$FILE" > /home/FileSystemCorruptionTest/`date +%Y_%m_%d_%H_%M_%S`_1.log
<<< "$FILE" has the same effect as using echo "$FILE" | before the loop but it doesn't create any subshells.
catthe file to the log file. What do you actually want to accomplish? Using a shell loop to process a file line by line is often something you want to avoid.