This might be old news for some of you, but I just figured this out myself. I was pushed into getting a solution by two fellow forum members and considering the three of us didn't know how to do this, I figured I'd make this a tutorial!
To answer an initial question: No, you cannot use Tapatalk, tinyurl, tinyimg, photobucket, etc. to upload your images onto the forum. If you want to research the background of that policy, there are several lengthy threads you can find in a search. That leaves you (intentionally) with one option: use the USMF's photo hosting feature. However, most phones take photos that are HUGE. Like 1.6 to 2.5 MB huge. Some people say "Well, they need to be that big so people can see detail!" No...not true. Normally, what happens is that people upload the massive image and when it's displayed, it looks like a pixelated blob (trust me, I'm on a forum that allows for up to 8 MB image uploads...quite often, you either have to make out what the image is from the thumbnail, or open the image, save it, and then size it down to see just what the heck it is...no...I'm not a fan of it...) Long and short of it is that you can upload an image smaller than 251 KB and it will be PLENTY for the forum. Image COMPRESSION is key. If you need help with that, there are also some good threads out there about that.
But back to images from a phone. I was very frustrated at the Show of Shows because I couldn't upload some images into PMs because they were too big. There might have been a few guys who missed out on some cool items because I didn't have their regular e-mail or phone number to get the image(s) to them. Kind of a bummer. Now that I've got this figured out...we're in business! And it works for PMs as well as for regular threads on the forum.
So here's how you do it. This is going to be a multi-step tutorial, and I'll put one image per post so I can comment on them for continuity.
Use your phone to take a photo. In this case, I took a picture of my shellback certificates on my office wall. This image is 2.02 MB. WAY too big for the forum!