I have never found that frankincense resin will melt into an oil base at the temperatures which the average person would use. Another solvent might work, however.
Try alcohol maybe, depending on your use,
but DO NOT heat the alcohol unless you absolutely know what you're doing. I made that error before & am lucky I didn't burn our condo complex down at the time
Alcohol will not be suitable for all products, so you might want to do both an oil infusion & a tincturing of the material, as one of my neighbours does to derive scents from wild plants. There is also the option of enfleurage, which I will be testing out soon as a means of boosting the depth of scent in my products, but I don't think this would be suitable for raw frankincense tears.
For frankincense tears / granules (you can buy them pre-ground in granules FYI which I do sometimes, making things less labour intensive) I grind them down with a mortar & pestle - freezing it is a spectacular suggestion which I will try - and then add it to a glass jar of base oil. Put a lid on which will prevent leaks.
I then put a dish cloth into a bottom of a stainless pot, put the jar in on top of that, then fill with water to the level of the oil mixture in the jar. This requires a pot which is as somewhat higher than your jar.
I then turn heat on low & infuse for 3-4 hours, checking water level every 30 minutes or so, topping that up
(HOT water because adding cool water can shatter the jar, which has happened to me before when not being mindful of this). I take the jar out every 30 minutes as well & give it a good shake. Use common sense as the jar is very hot.
At the end of the infusion period, I allow the infused oil to sit in the pot in the hot water & cool slowly to room temperature with a lid over top. This normally seals my jar, much like a canning jar seals. I'll then set it aside for a couple of weeks longer, or even a couple of months, giving it a shake as often as I remember to. There's also the option of vacuuming out all of the air from the jar while still significantly warm if it hasn't sealed, which can increase the amount of active ingredients pulled out of the plant material. This is something I do with my colorants that I cold-infuse.
Then it's ready to use. I just strain out the amount I require & leave the frankincense in the oil, giving it a shake now & again to avoid everything clumping up at the bottom of the jar.
I have not found that getting the same scent as the essential oil is possible this way as it's not a distillation, which is a very different process. The process outlined above is an oil infusion. Even with the essential oil, the scent you smell is different from batch to batch. It's a natural product, so you're not ever going to get the same thing time after time. You'll get something similar, but not identical. That's the nature of plant derived products. I deal with the same issue with all of my natural colorants & essential oils, even some of my raw materials derived from plants. For me, it's one of the amazing aspects of working with plants. I value working with them, rather than fighting them & their inherent nature / energy
Good luck figuring things out
