Treating separation anxiety in cyndaquil is very much like treating separation anxiety in any other pokémon, but in your case, it depends on how long you’ll be gone and whether or not cyndaquil is going with you. If you’re going to Kanto for a short time period and your cyndaquil will be staying behind, it’s important to get her used to either her poké ball (if you plan on storing her in the PC) or her caretaker (if not). If you plan on having someone take care of her, have them spend time with your cyndaquil. Give that caretaker your cyndaquil’s toys and treats and allow them to feed and play with your pokémon. If you plan on storing her, meanwhile, have her spend at least an hour a day in her poké ball. Start with only one hour, then increase the amount of time she spends inside until she has no problems with being stored. It may also help to switch the wallpaper of the box you plan on using to store her to something she might like; you could even let her decide. Each wallpaper is designed specifically to help a pokémon adjust to their stored environment, so choose something your cyndaquil finds comforting.
If your cyndaquil is going with you, it may also help to use poké ball training as well. Just as described above, have your cyndaquil spend some time within her ball each day until you leave. Then, when you get to Kanto, let her out in environments that she may be familiar with (such as a field or a wooded area—something that resembles even at a cursory glance the outside of your home) for increasing amounts of time until she grows used to being somewhere other than home.
It may also help to keep her out of the room as you pack, as the idea of you going away may be stressful for her, even if she’s going with you. Give her new toys to play with as you work and leave her in a separate room. If you’re not going to be taking her, it may also help to give her toys and leave her at home as you run short errands as well to get her used to you not being physically around. If she is going with you, be sure to take some of her old, more familiar toys as well in order to help her adapt to the new environment.
In short, the key is simply to train her to get used to different situations, depending on whether or not she’ll be going with you. Keeping your poliwag handy is definitely a good idea, but overall, it’s important to train her to get used to not only your absence (if she’s not going with you) or a new environment (if she is) but also, if applicable, her ball and her temporary caretaker.
Best of luck, anonymous!