Flutter + Posgresql based api with either Dart or Ruby on Rails

Hello, I am looking for a developer who has experience with flutter and building api. I have developed a ruby on rails website, but the controllers are not really coded in api starndard ways. I want to provide some basic features of the current site through flutter app. So for this I see that there are two options - one is to write APIs on ruby on rails. Or I see we could also possibly consider writing APIs with dart since we want to use flutter. Either way, we will be using PostgreSQL. I hope I can find someone who is a perfect fit for this project. Our budget is $200 for API side and $300 for the flutter side. We have screen designs on Zeplin. Requirements are as follows and the timeline is 1 week. I can work along-side to clarify any existing db models and design requirements. 1. Sign Up 2. Sign In (stay signed in) 3. Sign Out 4. Get push notifications about a match to other user, a task deadline set by other user, a message received, comments received 5. Create/Edit/Auto save/Save Letter model