How to calculate the output impedance of a adjustable RF amplifer to match the input of a mixer using SA605 chip
Your design problem is complicated by requiring tank resonance to vary from 88 - 108 MHz. Variable capacitance diodes might be used. These influence design choices for your variable-frequency tank.
If you go this route, the local oscillator tank resonance must be maintained 10.7 MHz above the RF amplifier tank resonance. Tracking these two resonant circuit frequencies is not easy. So tank bandwidth is often kept fairly wide.

Matching an RF amplifier to SA605 input (about 4700 ohms) is probably not worth the effort. An RF amplifier might have output impedance about a kilo-ohm or two. I'd just use a parallel-resonant tank in between and not worry about matching.