The denote-date-prompt-use-org-read-date option

By default, Denote uses its own simple prompt for date or date+time input (The denote-prompts option). This is done when the denote-prompts option includes a ‘date’ symbol and/or when the user invokes the denote-date command.

Users who want to benefit from the more advanced date selection method that is common in interactions with Org mode, can set the user option denote-date-prompt-use-org-read-date to a non-nil value.