It has nothing to do with Flash.
I don't have a Hotmail account, but I'm going to assume (hope) that it doesn't behave any differently when receiving attachments in Mail than any other account.
When you open the mail for the first time the PDF file is probably surrounded by a dotted line. This means that the file has not actually been downloaded from the server yet. Tap on the file. At that point it should start downloading. It will show you the progress of the download under the files name.
If the file is really big and you are on 3G, it may not download. At that point you might have to wait until you can get to a wifi spot.
Once it completes downloading the line around the file will be solid. At that point you have two options. You can tap on the file to open it in the default viewer, or tap-hold for a quick menu.
Tap-hold will present you with at least two choices (there may be more). Quick Look, which will open it in the default viewer, or Open In... which will give you the option of opening the file in a compatible app. What apps show up depends on what apps you have. Mine shows GoodReader, iBooks, and Evernote; all good apps to have.
If you are viewing the file in the default viewer you can tap on the share icon in the top right corner. You will get the same options as the other way, with the addition of the choice to Print. We won't go into that here.
To actually use the file outside of Mail you will have to choose one of the Open In... options. There is no general files system for you to save the file too and decide later. It must be associated with an app. Unless you already have an app you wanted to use the file in, GoodReader is one of the better choices for this. It has a file system, will view most file types, and you can use the Open In... feature to copy the file to other compatible apps as needed.
The other possibility is that the attachment shows up inline (viewable) in the body of the email. In that case it is already downloaded and should respond to tap and tap-hold just like the file icon did after the download was finished.
Finally, you mentioned a Download Button. Normally you would not have one of these, unless the email is an HTML mail (like a web page). Since you mailed the attachment to yourself, that seems unlikely. But if so, I'm not sure what to do. As I said, I don't have a Hotmail account to experiment with.
Let me know of this helps, or not.
