There are a few Daily Mail readers around here who might suggest following in the footsteps of the artists Gilbert and George and using human faeces to represent the EU!
But I'll try to be more positive. There are 27 member states, so a flag with 27 parts might be appropriate. However a flag which is 9 by 3 would look rather odd, so perhaps 28 blocks could be used (7 by 4), with each block representing a country plus an additional block to represent their union.
Simply using the 27 flags (plus another block as the representation of their unity) would just look a mess, so each block of colour needs to be placed alongside a similar one (or symmetrically opposite it). For example, blocks of colour (or individual flags) representing Slovenia and Slovakia can be placed symmetrically opposite to each other, as can those representing France and the Netherlands:
http://www.dreamstime.com/eu-flags-thumb4905365.jpg
How to make it? Possibly using a mixed thread fabric (such as a cotton/polyester blend) to represent how entities which are completely different can come together to offer both strength and flexibility at the same time.