I'm sorry you've not had much success here.
It can be very tricky indeed to introduce a new kitten to a home and for the 'settled' cat to accept them. This is particularly true if the 'settled' cat is used to being 'an only child', was a rescue and perhaps was not well socialised when younger. As the new cat is a kitten, this makes things even harder as they can be hyper and listen less to the body language of other cats.
While it may be the case that your Siamese will struggle to accept the new cat, there are certainly plenty of things that we can try before throwing in the towel.
While I understand the desire to introduce them immediately, this process needs to be a very slow one and I would not be tmepted to 'let them sort things out'.
Separating them at this point is essential to avoid any major fights, and they may need to be separated for some time longer.
First things first, prepare their territories. The new cat should have a designated area that is theirs and theirs alone; an area that has their own food bowl / water bowl / bed / hiding place / toys / litter tray etc. We cannot expect the cats to share ANY of their things at this stage, as this will likely only lead to conflict. Similarly, your established cat should have an area that the new cat is not allowed to go in to. When they understand their place in their home, they are less likely to invade each other's territory, creating jealousy.
After a few days, place your new cat in a new area of the house (with all the amenities it needs) and allow the Siamese to enter the new cat's old territory. They will be able to smell them and prepare for their meeting. Wait a few days while your Siamese cat gets used to the new smell and the idea of a new arrival.
You may also choose to mix their bedding at this stage, so they each sleep on the other cat's old bed. You can also stroke them separately without washing your hands in between, mixing their scents.
The next step is to allow them to smell each other through a closed door. If they both tolerate this well, the next day consider allowing them to 'meet' through some form of mesh/cat crate, so they are safe but can 'touch' and smell faces if they like.
If at any stage either of the cats show negative behaviours e.g. growling / hissing, take them back to the previous day's exercise. During their 'sniff sessions' it's great if they can each have someone with them who is stroking them and offering them treats so they understand it is all a positive experience.
Once you (and they!) feel ready for a real meeting, give them both access to a neutral room that neither of them sleep in or have belongings in. It's best to not have either cat picked up in your arms so they have the freedom to do what they choose. Ensure they each have an 'escape route', as well as high pieces of furniture or cat trees to run to. Quite commonly at this stage, once cat may choose to run away and hide. This is fine; let them take things at their pace & do not force a meeting.
The first few 'meetings' may only last a minute or two. This is fine, either cat may be finding things a little overwhelming.
In the initial few weeks, the cats should be supervised when together at all times.
Invest in a plug-in adaptor called 'Feliway Friends' which can be plugged in the wall and will release 'Happy cat pheromones' to encourage bonding.
Consider giving your Siamese a few weeks of calming supplements in their food to take the edge. These are safe, all natural products that can really help. Examples of brands include Zylkene and Nutracalm, though there are lots out there.
Though this process may take several weeks, most cats can learn to live in harmony.
Sadly, for some cats, they are really 'lone rangers' and may never fully accept having a buddy. Aiming for the cats to co-exist peacefully is a good place to start, as expecting them to bond and play is unlikely (at least in the first few months).
Going forward, do remember that even if both cats get along, they will not want to share their resources. They should each have one of everything they need, and there should be a minimum of 3 litter trays in the home (I know this can seem like an awful lot!).
A final option you have available, if the kitties are just not seeing eye to eye, would be to have a feline behaviourist come to your home to assess the cats and their environment. They may be able to offer some tailored advice.
Hopefully though, you will achieve good results before this becomes necessary.
