OK, first obvious question: Where did all the corners go? Did they get cut off? Is this sheet goods or adhesive tiles of some type? I think it is sheet goods from the pics.
Until I get a bit more info, here are a couple of ideas for ya. Short of starting from scratch, go ahead and glue down the flooring as you have it in the pics. If you have any extra scraps, cut some small triangles and glue them in with an over-cut procedure to assure no gaps in the solid color joint. Cut away some of the "grout" in the offending joint so you have at least an 1/8th inch gap, 1/4 inch would be better. After gluing and rolling the vinyl , let it cure a few hours, maybe a day.
Next: Get a quart of premixed synthetic grout in a matching color to the grout lines in the flooring. Apply the grout to the gaps with a plastic putty knife, wiping away excess from vinyl with a damp sponge. Try to get a nice even layer of grout into the gaps. It is important to get the synthetic adhesive style grout designed to be used with vinyl tile or CVT. This type of grout will stick better in a thin coat and does not need sealing later. After about 20 minutes clean all excess grout and haze from the vinyl. Be careful not to disturb the grout lines. After the grout has dried, finish cleaning any haze from the area with a damp sponge. Good Luck