Can I join different flooring to cover a height gap?
No you can't.   Well you can but you wouldn't be doing anything right.   There isn't a suitable transition piece that would hold up to use for tile to vinyl transition at an angle.   Actually the only way you can do angles is going from carpet to tile or tile to tile and while those work they aren't pretty and could be dangerous.

The easiest way to get with the is to flatten the area by the transition and let the rest of the kitchen run at a gradual angle.   There are a ton of ways you can transition this setup and you will probably just end up with a simple U channel metal strip - where the butt side is against tile and vinyl inserted into U.   

The other option is just to tile the who thing and use some kind of border tile to do the transition - again could be a trip hazard and isn't really right.   If you are selling the house soon it seems kind of dumb spending time to do something wrong when others will make you pay for it in the sale price.