Slack uses Markdown-style characters to format messages, along with keyboard shortcuts and a new rich text editor. That gives you several ways to strikethrough text in Slack:

• Add a tilde before and after your text: The quickest way to type strikethrough text is to type a tilde ~, then type your text, then close with another ~ like ~this~. Slack will then format that text strikethrough.
• Use the Slack strikethrough keyboard shortcut: CMD/Ctrl+Shift+X. Select your text, press that keyboard shortcut, and Slack will strikethrough that text.
• Use the formatting button: Select text and hover your mouse over it, and Slack shows handy formatting options—the S button will strikethrough your text. Or, if your Slack account shows an Aa button on the right of the text input box, click that to show the formatting toolbar to give you quick access to Slack's text formatting options. The S button will strikethrough your text.

There's no way to automatically show edited text as strikethrough, though, so you'll need to first strikethrough old text then add your new message if you want to retain the original message when editing things.