Agreed, its hard to get companies to financially sponsor you. But it is all about them them and them. What can you do for them, how do they benefit from giving you money, what is the potential return for them, etc. You really have to show them why they are benefiting from giving you money.
I guess you would need to also demonstrate why you in particular, perhaps not other badminton players, would make the company benefit from the sponsorship deal. Maybe you're very promising and have attracted media attentions. Maybe you have a special background or have special links which could be helpful for promoting your sponsor's public image, etc..
Here's how I would do it.
Inform why you want it(your story)
Point out your reach
how many followers you have on social media/your own website (twitter, facebook etc)
What tournaments you will be playing and the broadcast level including on site fan numbers.
How many people you coach and your influence.
Include potential direct benefits for your sponsor. (probably have to be businesses local to your living)
You could offer that you could do inspirational talks for the company (man following dream etc) for staff
or a team building day based around badminton or just straight up, some badminton coaching for the company.
If it is flights, why not try hitting up the airline companies? Of course things are much easier if you have contacts and any connection to any company you approach.