Because Gmail is a web-based system, you can't drag a file attachment from one message to another. As a workaround, you can do the following:
- Open the message or conversation that contains the file attachment.
- If the file is attached to a single message, click Forward (from the drop-menu at the top of the message). If it's attached to a message in a conversation, click Forward all on the right.
- Delete all the "forwarded" content from original messages, which appears at the bottom of your new message. Note that the file attachment remains with the forwarded message.
- Then compose your new message and send it.
Alternatively, you can download the attachment and then upload it to another message.