There is no Indian app in the cloud animation app market as of now. There are only startups who work in the animation service industry. So you're left with the option to choose from offshore cloud based explainer video apps as explained in my below answer.
You can buy the subscription for the VideoScribe using your debit or credit card. They have paypal as a payment gateway method. So you can simply use your debit card and sign up to the service. Paypal does the currency conversion on your behalf.
You have few options where you can buy the subscription using paypal in Indian currency.
1. Powtoon - This is similar to video scribe. They allow whiteboarding animation with audio to sync. You can use the app for both free and paid plans. This is more popular because they have some excellent video templates.
Powtoons premium plan has two options : 19$/month and 59/month. Each plan is pretty much the same but only the number of exports differs along with the storage size and quality of the file.
2. Rawshorts - Another company that accepts payment in paypal. You can use free option or paid plan. The paid option gives you more control over the content. The cost for the paid plan is based on the file format export.
Here is the pricing plans for the Rawshorts:
Pricing is based on the file export and you can choose the export plans in the range of 8$, 12$ and 20$. Subscription plans include 39$ and 49$ plan for small business and enterprise.
3. Animaker : This cloud based animation tool allows you to have various explainer board designs. Free plan has limit of upto 2 min of video. However the larger time will require paid plans. And those are also cheap in price. You can easily afford it for small projects.
Here is the pricing plans for the animaker.
Personal plan: 9$
Startup Plan: 9$
Business Plan: 39$
Pricing difference is based on number of files exported and the animated items used.
Please do note that the above subscriptions can be paid using your Indian debit card of any bank. Paypal allows such international transaction on cards from ICICI, Kotak, HDFC and AXIS bank.