Why I can't do a rest api request in Flutter
The issue is in your body parameters. You can only set a Map<String, String> to the body parameter, in your case it's Map<String, dynamic>.
According to http post documentation:
bodysets the body of the request. It can be aString, aList<int>or aMap<String, String>
For fixing it, convert your int type to String:
Map<String,String> data = { "title":title, "startDate":startDate, "startTime":startTime, "endDate":endDate, "endTime":endTime, "description":description, "city":city, "address":address, "entryType":entryType, "freePlacesCount":freePlacesCount.toString(),};