If you are shooting modern ammunition a separate "military approved" bore cleaner is a bit of an overkill. I have used G96 to clean firearms for over forty years, if there was a problem with this method I am sure it would have shown up well before now.
https://g96.com/product/gun-treatment/
Now with that said, after shooting suspected corrosive ammunition I will clean the firearm first with Ballistol, then oil with G96. However the only firearms I shoot with this type ammunition are belt feds and your question was about Thompsons.