When getting a new tattoo it is essential that you take good care of it. To do this you need to protect it from UV rays for at least two weeks, you should strive to protect it all the time as it can cause them to fade faster.
A dry skin cream such as E45 cream will need to be applied twice a day to stop the skin from peeling. If it is a big tattoo you may notice some flecks do come off but this is to be expected of large tattoos especially those on the arms.
Cling film can help to protect it and make the cream more conditioning, that way it doesn't rub on to your clothes.
After two weeks your tattoo should be fully healed and therefore you shouldn't have to be as careful.