Howdy Kathy!
Great question!! When you walk from Disney's Beach Club to Epcot, you will enter into Epcot via the International Gateway. Once you enter the Theme Park, you will head in the direction of the United Kingdom and Canada and then proceed to the front of the park through Future World. You will exit Epcot and catch the Monorail to the Transportation and Ticket Center. You will then get off that Monorail and take the Express Magic Kingdom Monorail, the Resort Monorail or a boat to Magic Kingdom. While it can be done via the monorail, if you are trying to make a dining reservation at Disney's Polynesian Resort, I would suggest taking a bus to Magic Kingdom and then either take the boat or Resort Monorail to the Polynesian.
If your final destination will be Magic Kingdom, give yourself an hour to get there. If your final destination will be the Polynesian, give yourself an hour and a half to two hours. This is extreme and I'm sure you won't need that much time but I want to ensure you make it to your reservation on time.
Just as a quick FYI, the walk from the International Gateway to the front entrance of Epcot is about 20 minutes depending on the crowd level.
You will love staying at
Disney's Beach Club Villas! Be sure to make time to enjoy Stormalong Bay. It's a 3-acre water wonderland that needs to be a must do on your list. It's phenomenal!
Thanks so much for your question and please let me know if you need any further information as you plan your vacation! Have a magical day!!