You can't really "stream" them. Transactions get confirmed once included in a block. So for 10 minutes you would have nothing and then all of a sudden there would be a 1,000+ transactions with a confirmation. If that's what you're looking for you can just use something like https://blockchain.info/block-index/$block_index?format=json and replace $block_index with the latest block. The json will respond with all transaction id's in an array that were included under "tx":

https://blockchain.info/api/blockchain_api

EDIT:
Blockchain.info has all the info you need. First get the current block height which you can get from https://blockchain.info/stats?format=json

$bcinfo = json_decode(file_get_contents("https://blockchain.info/stats?format=json"), true);
$latestblock = $bcinfo["n_blocks_total"];

Then plug the current block into https://blockchain.info/block-height/$latestblock?format=json

$getblock = json_decode(file_get_contents("https://blockchain.info/block-height/".$latestblock."?format=json"), true);    

Then just count the amount for each array and run a for loop to grab each input(from address) and each output(receiver) along with the time.

Here's one I did quickly in PHP: http://phpfiddle.org/lite/code/k16m-r8fh

<?php
$bcinfo = json_decode(file_get_contents("https://blockchain.info/stats?format=json"), true);
$latestblock = $bcinfo["n_blocks_total"];
$getblock = json_decode(file_get_contents("https://blockchain.info/block-height/".$latestblock."?format=json"), true);
$counttxs = count($getblock["blocks"][0]["tx"]);
for($i=0;$i<$counttxs;$i++){
    //tx time
    $timetx = $getblock["blocks"][0]["tx"][$i]["time"];
    $date = date('Y-m-d, H:i:s', $timetx);
    echo $date."<br>";
    //count inputs
    $countinputs = count($getblock["blocks"][0]["tx"][$i]["inputs"]);
    for($ii=0;$ii<$countinputs;$ii++){
        //get input address
        $addr = $getblock["blocks"][0]["tx"][$i]["inputs"][$ii]["prev_out"]["addr"];
        echo $addr ? "INPUT: ".$addr."<br>" : "";
    }
    //count outputs
    $countouts = count($getblock["blocks"][0]["tx"][$i]["out"]);
    for($iii=0;$iii<$countouts;$iii++){
        //get output address
        $outaddr = $getblock["blocks"][0]["tx"][$i]["out"][$iii]["addr"];
        echo $outaddr ? "OUTPUT: ".$outaddr."<br>" : "";
    }
    echo "<br><br>";
}

?>