Is it possible to calculate a number of years form the DOB and current date?

Yes it's possible 

Depending on your setup - I don't know what your layout is like

We need a lot more info from you on what you want to do and how it looks and how you want it to behave.

But basically

A script could work like this - you select the date formats you want to change 

whatever your date format might be

dd/mm/yyyy

yyyy-mm-dd

etc.

Then run the script - it inserts the age

And beside nonconforming date formats it will insert NaN - you probably don't want this

But the drop down lets you decide what your date format is which can be adjusted in the script

It's optional - you can just tell us the date format and we'll put it in that way - or you can adjust yourself

I notice it's not working entirely correctly - but can be fixed 

Run the script

It will work on every text frame (should do)

// Function to calculate age from birth date
function calculateAge(birthDate, dateFormat) {
    var today = new Date();
    var birthDateArray;
    switch (dateFormat) {
        case "dd/mm/yyyy":
            birthDateArray = birthDate.split('/');
            break;
        case "mm/dd/yyyy":
            birthDateArray = birthDate.split('/');
            break;
        case "yyyy-mm-dd":
            birthDateArray = birthDate.split('-');
            break;
        default:
            birthDateArray = birthDate.split('/'); // Default to dd/mm/yyyy
            break;
    }
    var birthYear = parseInt(birthDateArray[2], 10);
    var birthMonth = parseInt(birthDateArray[1], 10) - 1; // Month is zero-based
    var birthDay = parseInt(birthDateArray[0], 10);
    
    var age = today.getFullYear() - birthYear;
    var monthDiff = today.getMonth() - birthMonth;
    
    // If birth month hasn't occurred yet this year, or if it's the birth month but the birth day hasn't occurred yet
    if (monthDiff < 0 || (monthDiff === 0 && today.getDate() < birthDay)) {
        age--;
    }
    
    return age;
}

// Function to create a dialog box for selecting date format
function createDateFormatDialog() {
    var dialog = app.dialogs.add({ name: "Select Date Format" });
    with(dialog) {
        with(dialogColumns.add()) {
            var dateFormatDropdown = dropdowns.add({ stringList: ["dd/mm/yyyy", "mm/dd/yyyy", "yyyy-mm-dd"], selectedIndex: 0 });
        }
    }
    var result = dialog.show();
    if (result === true) {
        var selectedDateFormat = dateFormatDropdown.stringList[dateFormatDropdown.selectedIndex];
        dialog.destroy();
        return selectedDateFormat;
    } else {
        dialog.destroy();
        return null;
    }
}

// Main function to insert age at the end of each line
function insertAgesAtEndOfLine(textFrame, birthDates, dateFormat) {
    var lines = textFrame.contents.split("\r"); // Split text by line breaks
    for (var i = 0; i < lines.length; i++) {
        var age = calculateAge(birthDates[i], dateFormat);
        lines[i] += " " + age.toString(); // Add age at the end of each line
    }
    textFrame.contents = lines.join("\r"); // Join lines back together
}

// Function to process all text frames in a document
function processAllTextFrames(document, birthDates, dateFormat) {
    for (var i = 0; i < document.pages.length; i++) {
        var page = document.pages[i];
        for (var j = 0; j < page.textFrames.length; j++) {
            var textFrame = page.textFrames[j];
            insertAgesAtEndOfLine(textFrame, birthDates, dateFormat);
        }
    }
}

// Example usage
var document = app.activeDocument;

// Example birth dates
var birthDates = [
    "03/05/1989",
    "11/15/1976",
    "2000-07-28",
    "1995-02-10",
    "09/22/1982"
];

// Show dialog to select date format
var selectedDateFormat = createDateFormatDialog();
if (selectedDateFormat !== null) {
    processAllTextFrames(document, birthDates, selectedDateFormat);
}

Just an example.