Hi Amit,
Per my knowledge, there is no direct way to convert SharePoint server side web part to SharePoint hosted app form.
As an alternative, we can use Angular js to create custom SharePoint hosted app.
Here are some articles would be helpful:
Using Angular to Create a Dynamic SharePoint List Form:
http://www.threewill.com/using-angular-create-dynamic-sharepoint-list-form/
Developing SharePoint 2013 Apps using Angular.js:
http://www.dotnetcurry.com/sharepoint/1121/developing-sharepoint-2013-apps-angularjs
Knockout.js with Sharepoint 2013 App:
https://mysharepointlearnings.wordpress.com/2013/11/16/knockout-js-with-sharepoint-2013-app-i/
Thanks
Best Regards
TechNet Community Support
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