There's not a way to retrieve this data using JQL in Jira. There's an open feature request for it here: Ability to see Sprint start and end dates in search results in issue navigator
Please take a moment to vote for the issue, and if you're interested to know how we pick which features to implement, check out our New Features Policy
I understand this may be disappointing but there are some suggestions on how to get these details from the REST API - take a look at the StackOverflow posts Get the sprint list with start and end dates and How to get start and end dates of a sprint using jira api? for more info about the specific rest call. You might be able to get some of the information you need from here.
Here's the documentation for all of the Cloud REST APIs https://developer.atlassian.com/cloud/jira/software/rest/
Here's the specific one mentioned on StackOverflow: https://developer.atlassian.com/cloud/jira/software/rest/#api-rest-agile-1-0-sprint-sprintId-get
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