Creating a flash banner for clients is a project that I find myself doing quite regularly. And as there is a strict limit on the file size, I thought I'd share some of the tricks I've learnt along the way:

1. Use vector images as much as possible. Using graphics that aren't created in flash, or using lots of images is going to rapidly increase the file size. They also look poor when they have to be compressed to reduce the file size. The end result ends up looking like a cheap banner with poor quality and this is rarely the look clients are going for. 
2. Use as few different types of fonts as possible. Flash embeds fonts by each letter that is used. However the initial letter takes up a larger percentage of file size than the rest. For example using 10 letters - each using a different font is going to take up more bytes than 10 letters in the same font. Capitals and lowercase letters are also embedded separately, so if possible, using the same case throughout will save on size. As a general rule try to stick to just one font. Sometimes this is difficult because a design may have a fancy font and it needs to be complimented by a plain font. In this case try and stick with a system font for the plain font. They usually take up less file size than the fancy ones. 
3. Use flash generate size report to see exactly where the bytes are going. Flash has the option under Publish Settings to generate a size report. This is an extremely helpful report as it shows exactly where the file size is going, right down to the bytes. It doesn't not just include images, but also actionscript, tweening and embedded fonts.