I wrote a tools "Palindromer" to find palindromes in whole genome sequences. You can try https://github.com/jnarayan81/Palindromer . I am happy to improve it, if any features are requested.
Check out this GAP-Seq: a method for identification of DNA palindromes
https://bmcgenomics.biomedcentral.com/articles/10.1186/1471-2164-15-394