On Android, you can do it easily, but it's pretty well hidden.
First, copy your text as you normally would, then open the texting app. I still use Messenger, but some may think that's insecure.
Anyway, you should just be able to long press on the text window and select paste.
If you need to see it on your clipboard, just open the keyboard, just as if you are going to type, then look in the upper right hand corner for the Three Dot Menu. Press that, and a selection of items will appear. One will be you clipboard. You can copy and paste from that, or just clear the whole clipboard if you like.