I've emailed mobi files to my kindles hundreds of times.
Today, I created a mobi file for my new book by uploading the .epub to KDP, then downloading the preview file. When I emailed that preview to my devices, it never got there. When I used SendToKindle, it was uploaded fine.
If you are doing this to preview your book, be aware that the old mail-to system only forwards a Mobi 7 file. You won't know how the book renders in KF8 as used in most Kindles, Fire tablets, and apps today.
Instead, side-load the downloaded, so-called "mobi" (it actually contains both formats) from Step 7 in the publishing process.
I am using it to preview in this case, but in the future I want to supply the mobi file to several people (reviewers, for example), and have them be free to get it to their devices any way they want to.
Now, I can also create the MOBI file completely on my machine, using Kindlegen, and that one emails fine. It's also twice as large. I'm guessing that I'm going to have to supply that to reviewers, etc.
You download the "mobi" file at Step 7 in the publishing process. You can preview this in the (downloaded) Kindle Previewer. You can also connect your Kindle device through a USB cord (or wirelessly) to your computer, so it is just another drive on the computer. Using Windows Explorer or some other file-managing software, you go to the folder where your downloads are stored (probably called Downloads) and "drag and drop" it to the Kindle.
Alas, there may be many folders on your Kindle or tablet, so you must know what folder that your books reside in. On my Fire HD for example, I regret to say they are found in the folder /mnt/sdcard/books
I use a little app (I think I paid 99 cents for it) called Dooblou WiFi File Explorer. It connects right up and volunteers to download files from my computer. (I see the Fire tablet in a window of my Google Chrome browser.)
do not email mobi files to your kindle, that's just for pdf files.
Huh? It's always worked fine for me. I did get a bit lost when they stopped putting the books in the 'Books' folder and instead started putting them in the 'Docs' folder, but once I located them everything has been fine.
I create my mobi files from epubs using the freeware program Calibre.