Add 15 minutes to current timestamp using timedelta

You can achieve it just by using timestamp instead:

import time
from datetime import datetime

while True:
    # create a timestamp for the present moment:
    currentTime_timestamp = time.time()
    currentTime = datetime.fromtimestamp(
        currentTime_timestamp
    ).strftime("%Y-%m-%d %H:%M:%S")
    print "GET request @ " + str(currentTime)

    # create a timestamp for 15 minutes into the future:
    nextTime = currentTime_timestamp + 900  # 15min = 900 seconds
    print "Next request @ " + str(datetime.fromtimestamp(
        nextTime
    ).strftime("%Y-%m-%d %H:%M:%S"))
    print "############################ DONE #############################"
    time.sleep(900)  # call the api every 15 minutes

The output I got was:

GET request @ 2017-04-03 16:31:34
Next request @ 2017-04-03 16:46:34
############################ DONE #############################

You don't need to use datetime.fromtimestamp since nextTime is already a datetime object (and not a float). So, simply use:

nextTime = datetime.datetime.now() + datetime.timedelta(minutes = 15)
print "Next request @ " + nextTime.strftime("%Y-%m-%d %H:%M:%S")

Close. There is no need to use fromtimestamp here. You can reduce the last couple of lines to:

import datetime as dt

nextTime = dt.datetime.now() + dt.timedelta(minutes = 15)
print "Next request @ " + dt.datetime.strftime(nextTime, "%Y-%m-%d %H:%M:%S")

In other words, pass the datetime object nextTime as the first parameter to strftime.