To log FlexiCapture events you may use several ways:
Create common .Net script by using DateTime structure
DateTime currentDate = DateTime.Now;
Context.Field("Field").Text = currentDate.ToString();
See more details in the article Specifics of scripts written in .Net languages.
Use specific Data Source of the Service Fields
Here is the list of such sources:
Document creation time
Document export time
Document last edit time
Document recognition time
See more details in the article Service fields.
Use named registration parameters fc_Predefined:EmailDate for import from MAPI, IMAP or POP3 e-mail import
It is the date and time when the message was received.
See more details in the article Registration parameters.