For fishless cycling, test strips are fine unless you are using Amquel, Prime or AmmoLock2 for a water treatment. (In that case,the majority of other ammonia tests will give you false readings, too.) The presence of chloramine has no bearing on the accuracy of ammonia tests, be they strips or otherwise. The test will pick up ammonia in water with chloramine. The problem is when you use Nessler-based test kits (those with a single reagent, which includes most test strips) in the presence of ammonia-complexing conditions (Amquel, etc.). That type of ammonia tests will give false positive readings in the presence of ammonia-complexing conditioners.
One of the advantages of fishless cycling is that you don't have to be quite as precise in monitoring ammonia or nitrite levels. If you keep ammonia between 4-5 ppm, you'll be fine. As long as your test strips have been kept dry and haven't exceeded their expiration date, they should be sufficiently accurate to make sure you have ammonia in the tank and to be able to tell when it starts to decrease.
Fishless cycling is easy: just add enough ammonia once a day to bring the reading up to 4-5 ppm. After a period of time, you'll see a substantial drop in ammonia and a rise in nitrites. That means your cycle is progressing. If you read the stickies on this forum that describe the cycle, you'll know what to expect.
Good luck,
Jim