Can I avoid a big scar from the cut on my leg after a motorcycle accident?

Not if deep. Scarring is part of healing if the injury went below the dermal layer. You can make it less prominent by avoiding sun exposure, which will darken healing skin. Watch for infection, which will make a scar worse.
Avoid a big scar. A good deal depends on the initial trauma and how the tissue was repaired initially. What you can do is follow your doctors instructions. In general, it is best to keep the scar out of the sun. You may be advised to apply pressure to the scar or a silicon layer.
Scar managemnt. 1st month after tape scar at all times with medpor tape. After it is healed start massage with firm pressure several times/day. After a month add either a silicone scar cream (massage in) or silicone sheeting. Avoid sun on scars--very bad for them. If ur going to be in the sun wear spf 50 directly on the scar. Keep up with massage, cream or sheeting and/or taping for a year; sunscreen for life.
Yes. Laser rx cuts down the scarring process the otc products that contain allium cepa extract also helps.