Does vibrato a pitch mean that I will sound good?

Hi, Alex! Vibrato is usually a good sign: it means you've got breath support, cord compression, resonant space and relaxation. All of those things typically result in a good tone!

Will straight tone make my singing sound flatter?

It may make it sound flatter in terms of affect, but it shouldn't make you flatter in terms of pitch! Vibrato should oscillate both above and below the pitch you're singing, whereas straight tone does not oscillate.