I would be using rca to rca cable. The back of the Focusrite Solo has RCA connections (White and Red). My home stereo amplifier has an aux out rca connection. Would this work without damaging anything? I know that I must lower the volume of both interfaces first since I might damage them, Let's say if I did take this precaution, would problems still arise with this type of set up?
That sounds fine. RCA connections are always at line level so it should be matched correctly. The main thing you want to steer clear of is trying to connect the speaker outputs of your amplifier to anything that isn't a speaker.
The RCA connectors on the back of the Scarlett Solo are output jacks for speakers. I don't think they will function as inputs jacks for anything.
From the user guide (I suppose it's the scarlett solo)
Connecting Scarlett Solo to loudspeakersThe phono (RCA) outputs on the rear panel can be used to connect monitoring speakers. Self-powered monitors (i.e., typical computer speakers) incorporate internal amplifiers with a volume control, and may be connected directly. Larger, passive loudspeakers will require a separate stereo amplifier; in this case, the rear panel outputs should be connected to the amplifier’s inputs.
To connect to a stereo hi-fi amplifier you'll need to use a line level input. If yours has the classic TUNER/CD/AUX inputs they're ok. Also the TAPE MONITOR IN is good (except for some 70s amplifiers). The PHONO input it's not ok, because is for record player without internal preamplifier.
The only problem I could forsee is that the output is +10 dBU, so it could be useful to start with a very low volume. on the amplifier normally consumer level CD players have a +8 dBu output, and cassette decks are a bit less.