You can't have more than one component at the same time???

Couldn't get my text effects working so I made the text a movie clip instead and used a regular effect on it.
Then I added another Flash Eff component to a different layer on a different object. But as soon as it appears on the timeline, my first object with Flash eff disappears.
Now what's going on?

Probably you didn't added enough frames for the first effect to finish. You need to calculate the number of frames needed if you intend to use flasheff on multiple frames:
framesNeeded=showDelay+showTweenDuration+hideDelay+hideTweenDuration * document's frameRate.