"Would the net earnings I get (sales less cost less wtax) from the franchise still be subject to tax? "
Of course. BIR want to get paid
(if you earn enough to be above the free no tax amount per year.)
Except no income tax IF you get YOUR business approved as BMBE, which it isn't when it's a franchise or other biger organisation, but perhaps municipaly/barangay office say ok - wrong
- because of the franchise is in your cousin's name.
" Is there any form/ declaration I should provide on this agreement?"
That's why I suggest you DON'T start an own business (if you don't get BMBE).
Your cousin need to deduct the franchise cost from something. Otherwice that deduction will be WASTED.
So of these reasons it's better for you both the business go on in your cousin's name and he EMPLOY you with an only result depending salary, which you have agreed upon. (I suppouse your cousin get cover for the franchise cost and if there are any other costs, and perhaps you give him a bit more, and you get all the rest.)
Then you and your cousin only need to have acounting and tax forms filling for ONE business.
Then your taxes and fees are paid through your cousin's business.
If your part get good result, you can split it later, and move the franchise and space rent to you too then. You can include option for that in the contract you make with your cousin. Better make contract with your cousin even when being a cousin
so you know for sure what you have agreed to, to reduce risks for fights in the future. It don't need to be any complicated contract, write down what you agree to and what can happen in the future, sign and both of you have a signed copy each.
NOTE! Think of when you make the contract, part of the fees to SSS, PhilHealth and Pag-Ibig are paid by the "employer" so include in the contract giving your cousin compensation for that, so he don't get angry by it.
If you make your own business direct anyway, then make a contract anyway. Then your cousin make Invoices/reciepts to your business and you pay him for the franchise costs and other things he pay for your business. Then the results will be corect in both your businesses.