Flash is vector graphics based, so if you need pixel based, try Macromedia Director. You'd still need a pixel based program like PD to draw the animation frames in though.
It's pretty easy to use Director to add sound effects, right-click on a slot in the "Cast", choose Import. Drag the Cast member to the correct frame position in the Score, click the Play button. Has a silly limit of two sound channels in the Score
but maybe you can configure more.