I need to create an application that scans fingerprints and authenticates them. I can't find anything about fingerprint permissions on the Android website. Is it possible to use a phone's fingerprint scanner for a regular application? If so, what is the limit on the number of fingerprints it can store (I'd prefer to store them on the phone itself)
Thanks
Fingerprint scanner is not a feature in Android (Now available on Android M).
So each company as Samsung, Motorola, HTC create is own API and SDK to access to fingerprint sensor.
For instance Samsung provide a SDK http://developer.samsung.com/galaxy#pass
Pass SDK allows you to use fingerprint recognition features in your application. With Pass SDK, you can provide reinforced security, since you can identify whether the current user actually is the authentic owner of the device.
If you want to enroll multiple users and check users in your app, it's not possible with Samsung device. You could only check owner of device.
I don't know SDK of other companies.
UPDATE
Android M have new FingerPrint API: https://developer.android.com/about/versions/marshmallow/android-6.0.html#fingerprint-authentication
Android M preview introducing FingerPrint scanner API. You can checkout example for this here : https://github.com/googlesamples/android-FingerprintDialog/
I needed a similar functionality and my solution was to use an external scanner instead of use a device with integrated fingerprint scanner. There are several companies which offer integration with mobile phones through SDKs. You should research through out the next companies on google:
Nitgen: http://www.nitgen.com/eng/product/Hamster3.html#a2
Secugen: http://www.secugen.com/products/sdk_pro.htm#android
Tactivo: http://precisebiometrics.com/smart-card-reader/android/
In my case I used Secugen, but feel free to use the suitable device for your solution. Notice that this solution could make your project cheaper because you don't need to use an expensive mobile phone, the only feature that the phone needs it's having a USB OTG (On-The-Go).
I know this solution it's a bit different from what your were asking for but I believe that it could be interesting for you too.
You can opt to use an external Fingerprint Scanner and be able to Enrol Biometric Fingerprints from Persons you are Registering then proceed to save the Biometric Fingerprint Data and Person's particulars in your Android Phone. In my case I used a DigitalPersona type 4500 Fingerprint Scanner and used the Crossmatch API for Fingerprint Capture.
This is actually the easiest and feasible way for you if you want to succeed at Capturing Biometric Fingerprint Data and Save it in your Android Phone from more than one Individual. In fact what can limit you from enrolling more Biometric Data from various Enrollees will be the memory size constraints of your Android Mobile Phone / Device. This you can however easily circumvent by integrating your Android Biometric Authentication App with an external RDBMs Centralized Database of your Organisation like an MSSQL, Oracle, MySQL, PostgreSQL etc.
If it pleases you, you can choose to use the Source AFIS API to implement it with much ease. For motivation you can check out this project's web page here at [Android Biometric Authentication using External USB Fingerprint Scanner][2] that I developed [here][2].
See screenshots I have attached below for Fingerprint Authentication when the result is a MATCH FOUND and when the result is MATCH NOT FOUND. I have also included a screenshot for when FINGERPRINT ENROLLED.
I designed the User Interface ( GUI) that is reusable on Android Mobile Phone screens of various screen sizes for both Fingerprint Enrollment and Fingerprint Authentication. You can design your own interface anyway but in my case I wanted to be able to display the Person's Fingerprint during Authentication and I added an Activity for swapping Fingerprint Images on display after Finger Touch event is fired if Person places Finger on Fingerprint Scanner.
Happy coding.
[2]: https://jomutech.com/androidexternalfingerprintscanner/ 
Simple answer is NO.
But you can integrate it by Implementing Google's fingerprint recognition introduced in Android M which only supports 5 attempts at a time, if all the attempt fails your device finger print reader will be blocked for 30 seconds, then after that duration you can authenticate with the fingerprint again.
For example you are using an 2 app(A & B) with finger print support. Then you enter 3 incorrect fingerprints and then you close the app A, then you open the app B so there are total 5 attempts available within 30 seconds so your app can only authenticate 2 times because app A took 3 attempts hence after 2 unauthorized attempts the OS blocks the reader for all apps.
So wait for 30 seconds or ask the user to enter pin or passcode accordingly if the user doesn't wants to wait for that amount of time.
Hope this helps.
