I have two suggestions:
If you do it right, tape is probably the healthiest DIY binding technique. The trick is to use paper tape, like painter's tape, first and then go over it with duct tape. This ensures that your skin won't rip from being pulled off.
Also, don't just wrap it around your chest, put a vertical strip on each nipple and then use longer strips crossing over that strip and pulling back and up, and anchor it to your shoulder blade. This technique doesn't compress your chest, and if you use painter's tape beforehand there is minimal risk of ripping your skin. You can also use this method if you want to show more chest, like unbuttoning your shirt if it gets hot, because your boobs are flattened to the sides and not the front. Drawbacks are that it can get itchy and takes a long time to do, and if you have an allergy or have sensitive skin it can cause a rash.
Another way I've found to be very helpful is by taking control-top tights or compression shorts, cutting the crotch out of the middle, and cutting the legs off and wearing it like a sports bra. You may need to trim it a little to fit properly, and the shoulder straps can sometimes dig in to your shoulders, so you may need to put some padding (i.e. a small sock) between it and your shoulders. Also, the armpit area is a place that is easily chafed. When cutting the crotch, make sure to leave one edge of the stitching attatched and one separated, to ensure that it will be sturdy enough but you can also fit your head in.
Also, as with any binding technique, make sure you listen to your body. If you start to get chest or back pains, or find it hard to breathe, or get lightheaded or dizzy, TAKE IT OFF. There can be serious complications involving heart attacks, strokes, paralysis, pneumonia, broken ribs, etc. if you don't listen to your body. Don't bind when you go to bed, either, because you won't be able to get out of your binding in time to have yourself.
Hope that helps! <|:)