First off: flooring first, baseboards later.

Secondly and more importantly: tile over tile is SUPER risky. It *can be done. The question becomes "should" it be done? The answer is "No," it shouldn't.

It costs $1 - $2/sf to remove tile. That's a decent "guarantee" to have better results. Whenever you attempt to put down new "permanent" flooring over old, you have to rely on the OLD stuff holding on (grabbing and staying put) for TWICE as long as it is designed to do. Imagine if the lifespan of a tile floor is 25 years. Now imagine you put a new floor over top of an 23 year old tile floor. Do you believe you will get ANOTHER 23 years out of the ORIGINAL tile/mortar?

No probably not. You might get another 10. And imagine how upsetting that would be to have to pay all of that AGAIN...simply because old tiles were left in place.

Technically it can be done. Most tilers with a reputation will not want to do it. You, the owner, would have to FORCE them to do it - and you sign a waiver for good measure.

Tile before baseboards always. I would not tile over tile.