Add a file input -> the users taps it -> ios asks if they want to use an existing photo or take a new one -> take a new photo. Result on android may differ.
I don’t use Instagram so can’t check the code, but I would guess they use something like
<input type="file" accept="image/*" capture>
Which does what you’d expect on a mobile device (launch the camera) but behaves differently on desktops (opens a file upload dialog). They may have decided that this behavior would confuse users.