Why don’t I have a Find my iPhone icon??

If you have updated to iOS 13 it is going and replaced with the Find My app.

Assuming your phone is okay and also Find my iPhone app cannot be deleted it may be hiding with another app, this happens sometimes by accident.

Tap each app one at a time to see if it got joined to another app, if you find it just drag it out.

Is your iphone updated to iOS 12 or iOS 13?

Should be the latter:

In iOS 13 or later version, there is a new app called "Find My", which contains (and replaces) Find My iPhone and Find My Friends apps.

See this page for more info:-->  Find My – Official Apple Support

This new app is already available on your iPhone (if updated to iOS 13 or later). This is the related icon:

You should be able to locate it:

in the same position where Find My iPhone icon was (using iOS 12);

or in Extras folder (or a different folder);

and in Settings>[your name].

Regards

Giulio