We're slowly in the process of replacing the flooring in our kitchen with vinyl tile. Half the kitchen was carpeted and half had ceramic tile. Under the carpet was THREE layers of vinyl tile and linoleum ! Under the ceramic was only one layer of linoleum. Anyway, we removed everything down to the subfloor, 1/2 to 3/4 plywood, which in turn sits on approx 3" wide "planks", which sit on the floor joists. My house is close to 100 years old so I presume it's typical for construction of that era.

On top of the subfloor, I put down 1/4" underlayment. I left 1/8" gaps between the sheets. Due to my skills, or lack of, some pieces that I had to cut and fit have larger gaps. One, for example, is approx 1/4" wide but only about 4" long. Regardless, I want to fill these gaps, do I not ?? And if so, with what ?? We bought Armstrong S-194, Patch,. Underlayment, and Embossing Cement but I'm not sure it's the right stuff. The instructions do say that vinyl tile, doesn't specify self-sticking or glue-on type, will bond to it, which I was very unsure of. I guess it helps to read the instructions !!

So again, do I need to fill all of the gaps ?? Or only fill the "bad" ones ?? What do I use to fill them ??

 

I'm doing the same thing but to a bathroom. Have my underlayment ready to cut and put down (1/4-inch underlayment plywood from Multipleply Plywood sold at Lowes for $12 a 4x4 sheet. I am going to use Armstrong tiles, and am not going to leave ANY gaps anywhere in the underlayment unfilled.

If I had a little piece like you have I would make a plug out of the underlayment leftovers, nail down the plug, and fill the gaps.

Be sure to sand all filled gaps smooth as a baby's ass. Anything protruding will telegraph right up through the vinyl.

Good luck.