Is it permissible to advertise a motorcycle that is not mine, and then buy it from a family member after they agreed to sell it to me for a certain price. Then sell it to a buyer who would give me more for the motorcycle. I will be buying it before I make any sale on it regardless.

Advertising it is fine as long as you agree no sale with anyone until you have bought it and taken full possession of it, and then you may sell it for whatever price you agree. Selling it, or fixing the deal with the buyer, before that is selling what you do not own which is not allowed.