It doesn't make sense that the yellow blob is a current sink:
If it were a current sink, then there would be no point to the resistor in series with it. That only wastes power, reduces the compliance range, and doesn't change the current.
You need to look at the whole circuit to see what is really going on. If I were designing a LED flashlight, I wouldn't boost to a regulated voltage, then linearly regulate to a fixed current from there. It makes much more sense for the boost converter to regulate its output current directly.
Yes, it [R1] is 1 ohm. Before I reverse engineered the circuit I thought it is current sense. But it is not. I changed it to 0.5 ohm and current did not change. Then I reverse engineered schematic. I assume it is there to limit the current in case that driver failed.
1 Ω wouldn't limit the current much. Besides, what would be the point? The current would only go too high if something else already failed. This is a small device that nobody is going take apart to service. It will simply get tossed when it fails. Preventing one failure from causing another failure doesn't make much sense.
Another possibility is that R1 spreads the heat dissipation of the current sink. At 90 mA, it will drop 90 mV and dissipate 90 mW. That 90 mW is a significant fraction of what a SOT-23 can dissipate, which is usually around 120 to 150 mW. If the max current sink dissipation were 200 mW, for example, then the SOT-23 probably couldn't handle it. But with R1 taking 90 mW, the SOT-23 can handle the remaining 110 mW.
However, this is a stretch too. Why not simply regulate the voltage to 90 mV less in the first place?
This points out the overall problem of trying to drive an LED with constant current from a constant voltage source. A better answer is to have the boost converter regulate to the desired LED current in the first place.
General LED flashlight discussion
See my KnurdLight LED headlamp for an example of regulating the LED current directly. This project uses four 20 mA white LEDs in series instead of a single 90 mA LED. The LED string voltage is therefore higher and the current lower, but the concept is the same.
Here is a snippet of the schematic showing just the boost converter and the current sense:
The boost converter is formed by L1, Q2, D1, and C1. The battery voltage is directly applied to the left end of L1. In this case, I used two AA batteries in series, for about 3 V nominal. However, due to the current regulation, this works down to about 1.8 V while keeping the LED current reasonably constant.
R6 is the current feedback resistor. The voltage across R6 is compared to a 600 mV reference, which is then used to decide when another boost pulse is needed. Note there is no attempt to create a regulated voltage anywhere. The voltage across the LED string comes out to whatever is required to keep the current at 20 mA. That's typically about 12-13 V, but varies with temperature.
Additional feedback not shown in this snippet might appear to regulate the voltage, but that's only to prevent the voltage from going too high in case the LEDs get disconnected. Sufficiently high voltage on the P1 output will shut down the boost converter. But, that's not intended to ever happen during normal operation.
Current sink drivers
The above explains why you are asking the wrong question. However, I'll answer it somewhat anyway. There are chips designed to be constant-current sinks for driving LEDs. I don't know if any exist with single outputs in a SOT-23 package, since I've never looked for such a thing. I have used such chips for driving many indicator LEDs from a single microcontroller.
The ST Micro STP16CPC26TTR is one example I have used. It has 16 current sink outputs. The data is clocked in serially, and multiple of these chips can be strung together into a single shift register. This allows a large number of separate indicators to be driven with only three control pins.
I used 9 of these in a recent project that included a 40-LED bar graph, six 15-segment alpha-numeric character LEDs, and a few miscellaneous individual indicators. It all worked very nicely. To keep power consumption low, I created a separate voltage supply that was just enough for the worst case voltage across the LEDs, plus the little bit the driver needed to perform the current regulation. It saved a couple of Watts of worst case consumption compared to the previous version (not my design), that just used the existing 5 V supply to drive the LEDs with.
However, again, this is not really useful for a flashlight due to the lower efficiency.