Best blankets to help soundproof my bedroom door?

Forget soundproofing, all you can hope to do is make the noise less intrusive. Traditionally you had a baize covered door to separate the service areas froom the house, but that was all different construction. Hang a strong curtain track, as you would over a window (corded for preference) Then make a heavy, interlined curtain using acoustic quilting and hang to cover the door, frame and onto the wall, and let it sit on the floor. (You don't need a sewing machine to make curtains). You need to open the curtain(s) to use the door. In the days of coal fires you could attach the rod on stalks off the top of the door so the whole curtain moved with the door. Investigate making the kitchen door self-closing to stop the noise breakout at source.

MASS is the key. No blanket advertised as 'sound proof' is actually any better than any other blanket that is the same mass.

Putting up a think "blackout curtain" on a rod covering the door, or padding the door itself, also mounting two doors are used.
Best, least expensive, is to use a Smart TV or Radio set to a 'cover' (aka canceling) noise. [That is what I use.]

Going to bed when you are "falling down" tired works too.

Nothing is going to soundproof it because of the fact that there is a small space on every side of the door.

Unless you put up a curtain rod and drape heavy wool blankets over it and then move them aside everything you want to open the door.

Ask the people who use the kitchen to not clank so much.

A heavy quilt.  Maybe a sleeping bag.

Ear plugs or ear phones if you want to listen to music WORK.  Get industrial type plugs that you first roll into a point and then stuff into the ear.  The heat from the body expands the foam making a tighter fit.  Welding shops use them as they bang on heavy metal.  Combine that with ear phones and you will be hearing very little from the kitchen.

Cheaper too.

Use acoustic foam on the outside of the door to absorb the sound waves 

No blanket will sound proof door.

What about ear phones, ear plugs, ear buds.

Low music on

Help clean up dishes before you go in room.

Move to another room