How to get raspberry flavor into a smoothie without seeds?
There are a couple common ways to deal with seeds in berries:


Use a food mill, which uses a rotating blade to crush the berries and force them through small holes. They're designed for this sort of thing - removing seeds or large pieces of pulp.
Do what the food mill does, but by hand: push them through a reasonably fine strainer/sieve. Unless they're really soft, you generally want to puree them first. You can also incorporate other ingredients first, to give more liquid to work with, so you don't have to do as much pushing.