Flickering lights must be addressed straight away. Loose wires can cause heat and with heat can come fire. Not only that but the power drop could be causing damage to appliance motors like the washing machine. Circuit breaker finder article.
Often single light fixtures with loose rivets in the bulb socket flicker, but is more serious when more than one is acting up. Besides causing the light to flicker, bulbs do not last very long due to the surging electricity.
Your first step will be to find the loose link in the system causing the voltage drop. Are the effected lights on the same circuit breaker? If you turn off the circuit breaker that controls the kitchen lights, do the basement lights go out? If they do, what of the washing machine? Test it with the breaker off; is it on the same circuit?
If everything is on the same circuit breaker, you may have the answer to your problem. Here is the big question, are you comfortable turning off the main breaker and removing the circuit breaker in question? If you are, you may need to go to a store with circuit breakers and get a replacement. While you are there, get a hands-on explanation on how to safely remove and replace your brand of breakers. With this in mind, get the brand and model of your electrical panel before you go. Yes, these things are brand specific and are not universal.
Be sure to disconnect the power when working with any electricity. For extra safety, use good quality, well insulated tools. Wear dry rubber soled shoes on a dry surface, and do not use an aluminum ladder.
When you are ready to disconnect the wire from the old breaker, first try to tighten the screw holding the wire. Was the screw loose? If it was, the breaker may not have been bad after all. Tighten the wire and reinstall the breaker.
This may not be where the problem is even if all the effected appliances are on the same circuit. There may be a junction box where wires meet and are joined with wire nuts. The loose connection could be in one of these not in the electrical panel after all. Checking the boxes with the power off and tightening all the wire nuts might solve the problem. The problem could also be a receptacle in the middle of the circuit that has loose connections.
What if your lights and the washing machine are on separate breakers? This will take the solution to the next level of expertise. Leave tightening lugs on the main wires from the electric meter to an electrician. Not only that, but the last situation I had like this, the problem was with the power company. They had a loose connection up on the pole and it was not in the house. The loose wire was only on one of the wires feeding the house, so only half of the house was having problems. The other half was working with no apparent problems.
Whenever dealing with electricity, be safe, sane, and never take chances when you are not sure of what you are doing.