Chances are you haven't tried hard enough.
Sorry to be so blunt, but it's bothersome when I can do it fine yet people claim it's magically impossible to post a video while on mobile. Here is you miracle cure or whatever you want to call it:
So as long as your video is on youtube that's great. For vimeo and all the other accepted websites I'm not quite sure yet, however I'm sure you can figure it out.
Main things to remember while posting video. These are your greatest friend. [video ] and [ /video] remove the spaces and insert the youtu.be short link in between, almost like posting an image. With the [img ] and [ /img] things that make magic happen on the internet.
I know some of you may be wondering "Lé.skiing, how do we find this mystical youtu.be link?"
Well, curious NSer, I'll tell you.
As most of you know already that you can find the youtube short link here in the average computer browser.
(image for reference)

(Need to click {weird unfinished triangle or less than} symbol to unlock the secrets of the shortlink)
Well on mobile it can be a little bit more tricky than that. However it it still possible to obtain the secret short link that youtube yields. If you have the option to share a video via text. Do it(but don't quite complete it.)
How to get there:

Choose to send Via Text message.(I'm sure you can figure that part out.)

Copy what I have selected in image shown above. Voila that is what you paste in between [video ] and [ /video] Just remember to remove the spaces.
I feel as if that's all that needs to be said about it.