Trying to check it yourself will likely be unsuccessful and could even damage the transmission. Do not attempt to remove any plugs or access ports related to the transmission yourself unless you are a qualified mechanic.
If you suspect a problem with your transmission fluid (e.g., slipping gears, rough shifting, unusual noises), you should take your Chrysler 300 to a qualified mechanic or dealership for diagnosis and service. They have the proper equipment and expertise to properly assess and address any transmission issues.