If it were me, I would:
1. Sneak some sheet vinyl flooring adhesive under that tear with a small brush as best you can, and allow time for it to get tacky. Press the vinyl down.
2. Cover the repair area with a piece of wax paper about the size of the sheet metal you have.
3. Put a piece of sheet metal over the sheet vinyl and wax paper (or several pieces of steel) that will lay flat on the floor.
4. Beg, borrow or steal an electric blanket, fold it up and put it on the sheet metal
5. Put a piece of plywood over the electric blanket, and
6. Put something heavy, like a 5 gallon pail of water, on the plywood.
Turn the electric blanket on HI and leave it overnight light that.
The heat from the electric blanket will soften the vinyl and coax it to lay flat under the metal. As it flattens, the tear should close up. The glue under the vinyl will stick the vinyl down the way it was. Warm glue will flow under the vinyl so the floor should lay as flat as the sheet metal.
The wax paper is to prevent any rust or dirt on the metal from sticking to a warm soft vinyl or warm soft polyurethane wear layer on the floor.
If the tear is still noticable as dark lines on the sheet vinyl, then use masking tape to tape off the dark tear lines, fill those lines with a beige, grey or almond coloured acrylic or silicone caulk to match the floor colour as best you can, wipe the caulk down with a finger dipped in a 50/50 solution of liquid dish washing detergent and water, pull the masking tape off and allow the caulk to cure before cleaning the dish washing detergent off the floor.